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Jehan Oh

Publications and source records attributed to Jehan Oh.

At least 19 recordsLinked to original sources
arXiv2026

Local boundedness for solutions to parabolic double phase problems

In this paper, we investigate the local boundedness of weak solutions to parabolic double phase equations of type $$u_t-\mathrm{div}(|Du|^{p-2}Du+a(x,t)|Du|^{q-2}Du)=0\quad\text{in }Ω_T:=Ω\times(0,T),$$ where $0\leq a(\cdot)\in L^\infty(Ω_T)$ and $\frac{2n}{n+2}<p<q<p\left(\frac{n+2}{n}\right)$, so that both the degenerate range $p\geq 2$ and the singular range $p<2$ are covered. To this end, we derive the Caccioppoli inequality and recall a parabolic embedding theorem, which are then utilized in an iteration method.

math.AP↗
arXiv2026

Sharp asymptotics for a free boundary touching a degenerate boundary: the perpetual Heston put

We study the exercise boundary of the perpetual American put in the Heston model near zero variance. There the pricing operator degenerates, and the exercise boundary, a free boundary in the stock--variance half-plane, touches the boundary of the half-plane. No Feller condition is imposed. The boundary is analytic at positive variance and extends as a regular $C^1$ curve tangent to the zero-variance axis. Its approach to the axis follows one of three laws, according to whether the Feller ratio $2κθ/σ^2$ is larger than, equal to, or smaller than one: a logarithmic correction to linear order, an exponential correction in the square root of the logarithm, or a fractional power. In the first two cases the leading coefficients are explicit and the tangent is not Hölder continuous at the axis. In the third case the exponent is selected by a possibly nonsymmetric stable operator on the axis, and the amplitude is finite and positive.

math.AP↗
arXiv2026

Optimal $C^{1,α}$ regularity up to the boundary for fully nonlinear elliptic equations with double phase degeneracy

In this paper we establish optimal $C^{1,α}$ regularity up to the boundary for viscosity solutions of fully nonlinear elliptic equations with double phase degeneracy law and oblique boundary conditions. The approach developed here relies on first deriving uniform boundary Hölder estimates for perturbed models with oblique boundary data in ``almost $C^{1}$-flat'' domains. Building upon these estimates, the desired regularity is obtained through a compactness and stability framework for viscosity solutions. As a byproduct of our analysis, we determine the optimal Hölder exponent for solutions when the governing operator is quasiconvex or quasiconcave. In addition, we establish an improved regularity result along vanishing points of the source term.

math.AP↗
arXiv2026

Interior smoothness and zero-variance geometry for finite-maturity Heston American puts

We study finite-maturity American puts in the Heston model without the Feller condition. At positive variance, the exercise boundary is smooth and strictly decreasing in remaining maturity and variance. At zero variance, the endpoint is locally Lipschitz in remaining maturity, the boundary moves with bounded speed in maturity uniformly down to zero variance, and it extends continuously to the axis. Each boundary slice at positive maturity has a regular $C^1$ closure tangent to the zero-variance axis, its stock threshold has variance derivative tending to minus infinity, and both partial derivatives of the inverse boundary graph vanish along the slice. The continuation premium at the axis contact stock is of order variance, and as a consequence smooth fit fails in the variance direction at the axis. At expiry the whole boundary, including its axis edge, converges to the strike. We give quantitative boundary gap bounds, an exact limiting weighted boundary Hessian, and vertical identities retaining the maturity term. Exact boundary gap equivalents remain open.

q-fin.MF↗
arXiv2026

Borderline double phase functionals with powers of the logarithm: regularity in the vectorial case

We study vector-valued local minimizers of the borderline double phase functional whose integrand is $|D\mathbf{w}|^p+a(x)|D\mathbf{w}|^p\log^γ(e+|D\mathbf{w}|)$, where $p>1$, $γ>0$ and the coefficient $a(\cdot)$ is nonnegative and bounded. If the modulus of continuity $ω(\cdot)$ of $a(\cdot)$ satisfies $ω(r)\log^γ(1/r)\to0$ as $r\to0$, then minimizers are locally Hölder continuous for every exponent less than one. If $a(\cdot)$ is Hölder continuous, then the gradients of minimizers are locally Hölder continuous. In the vector-valued setting these results were previously available only for $γ=1$. The proof combines a comparison with frozen functionals, whose regularity theory applies uniformly in the frozen coefficient, with the higher integrability of minimizers.

math.AP↗
arXiv2026

Consumption adjustment with mean-reverting risk premia: A singular stochastic control approach

We study a two-sided singular stochastic control problem in which changes in consumption carry utility costs and the risk premium follows the mean-reverting Kim-Omberg model. Optimal consumption is reflected between two moving barriers given by thresholds that depend on the current risk premium. These thresholds are the stopping boundaries of a Dynkin game for a two-dimensional diffusion driven by a single Brownian motion. A sharp occupation estimate shows that they are Lipschitz in logarithmic scale, uniformly in the cost of reducing consumption, and that smooth fit holds along the diffusion direction at every contact point. Outside a bounded interval of risk premia and at most two further points, the thresholds are infinitely differentiable. As the reduction cost grows, optimal consumption converges to the ratcheting policy.

math.OC↗
arXiv2026

Gradient estimates for generalized double phase problems with two modulating coefficients

We prove local Calderón-Zygmund estimates for distributional solutions to non-uniformly elliptic equations in divergence form modeled on the energy density $a(x)G(|z|)+b(x)H(|z|)$, where $G$ and $H$ are Young functions and $a(\cdot)$, $b(\cdot)$ are nonnegative coefficients, Hölder continuous with exponents $α$ and $β$. Either coefficient may vanish, and only their sum is bounded away from zero, so that each phase can dominate or disappear. Under a gap condition that reduces to $q/p\le1+\min\{α,β\}/n$ for $G(t)=t^p$ and $H(t)=t^q$, including the borderline case of equality, we show that the energy density of the gradient inherits the Orlicz integrability of the energy density of the datum. The proof combines a fractional differentiability estimate, which gives higher integrability up to the borderline growth, with comparison arguments that freeze the two coefficients in the appropriate order.

math.AP↗
arXiv2026

Regularity for vectorial double phase functionals with two modulating coefficients and logarithmic-type growth

We study vector-valued local minimizers of double phase functionals with two modulating coefficients and logarithmic-type growth. The energy density is $a(x)|Du|^p+b(x)|Du|^p\log(e+|Du|)$, where the nonnegative coefficients $a(\cdot)$ and $b(\cdot)$ may vanish but their sum is bounded away from zero. Assuming that $a(\cdot)$ is uniformly continuous and that $b(\cdot)$ satisfies a vanishing log-Hölder continuity condition, we prove that minimizers are locally Hölder continuous for every exponent in $(0,1)$. If both coefficients are Hölder continuous, then the gradient of a minimizer is locally Hölder continuous. The proof combines Gehring-type higher integrability with a comparison argument.

math.AP↗
arXiv2026

The Hölder interpolative gap bound for degenerate parabolic double phase problems

We study weak solutions to degenerate parabolic double phase equations with growth exponents $2\le p<q$ and a modulating coefficient that is Hölder continuous with exponent $α$. If the solution itself is Hölder continuous with exponent $γ$, we prove higher integrability of its gradient under the gap condition $q\le p+α/(1-γ)$ together with $q<p+1$. This is the first gap bound of Hölder interpolative type for parabolic double phase problems, and it is the parabolic counterpart of the corresponding bound for elliptic problems. For $α<1$ it allows exponents beyond the range $q\le p+α$ known for bounded solutions.

math.AP↗
arXiv2026

American condor contracts with a cash component: A variational inequality approach

We study a jointly exercised American condor contract whose payoff is a call condor payoff plus a positive cash amount. Its plateau and positive tails produce two inner exercise boundaries and two outer cash-exercise boundaries. We construct the unique bounded solution of the associated variational inequality, strong on each side of the plateau, and identify it with the optimal stopping value. We prove monotonicity and continuity of the four boundaries and determine their limits at expiry. Following Broadie and Detemple, we express the inner boundaries as cutoffs of the boundaries of uncapped contracts with the same cash components. We also prove call-side convexity and volatility monotonicity under a sufficient condition, solve the stationary problems explicitly and present numerical results.

math.AP↗
arXiv2026

Regular specular differentiation in Euclidean spaces

We study the regular specular derivative, a generalized derivative defined at every point where both one-sided derivatives exist and are finite. Geometrically, it is the slope of the mirror that reflects the left tangent ray into the right one. In one variable we derive computational formulas, prove inverse function and rotation rules, establish Quasi-Rolle's Theorem and the Quasi-Mean Value Theorem, and obtain a derivative-limit theorem, which shows that twice regularly specularly differentiable functions are continuously differentiable. We also prove both parts of the Fundamental Theorem of Calculus. In several variables we introduce specular gradients, directional derivatives, tangent hyperplanes, and normal vectors, show that a continuous specular gradient forces classical differentiability, and characterize when the specular tangent hyperplane is unique.

math.CA↗
arXiv2026

Absence of the Lavrentiev phenomenon for a general class of parabolic double phase problems

In this paper, we prove the absence of the Lavrentiev phenomenon for a general class of parabolic double phase functionals with Orlicz growth. The energy density is given by $$ G(|Dw|)+a(x,t)H(|Dw|), $$ where $G$ and $H$ are Young functions satisfying the $Δ_2$ and $\nabla_2$ conditions with $G\prec H$, and $a(\cdot)$ is a continuous nonnegative coefficient. Under suitable balance conditions between the growth gap of $G$ and $H$ and the modulus of continuity of $a(\cdot)$, we show that every finite-energy map can be approximated locally by smooth functions without loss of energy. The result extends the known parabolic double phase theory from power type growth to a broad Young function framework and identifies the natural space-time Orlicz energy class for the problem.

math.AP↗
arXiv2026

Gradient higher integrability for degenerate parabolic double phase systems with two modulating coefficients

We establish an interior gradient higher integrability result for weak solutions to degenerate parabolic double phase systems involving two modulating coefficients. To be more precise, we study systems of the form \[ u_t-\operatorname{div} \left(a(z)|Du|^{p-2}Du+ b(z)|Du|^{q-2}Du\right)=-\operatorname{div} \left(a(z)|F|^{p-2}F+ b(z)|F|^{q-2}F\right), \] where $2\leq p\leq q < \infty$ and the modulating coefficients $a(z)$ and $b(z)$ are non-negative, with $a(z)$ being uniformly continuous and $b(z)$ being Hölder continuous. We further assume that the sum of two modulating coefficients is bounded from below by some positive constant. To establish the gradient higher integrability result, we introduce a suitable intrinsic geometry and develop a delicate comparison scheme to separate and analyze the different phases--namely, the $p$-phase, $q$-phase and $(p,q)$-phase. To the best of our knowledge, this is the first regularity result in the parabolic setting that addresses general double phase systems within the framework of weak solutions.

math.AP↗
arXiv2026

Interpolative Refinement of Gap Bound Conditions for Singular Parabolic Double Phase Problems

We consider inhomogeneous singular parabolic double phase equations of type $$ u_t-\operatorname{div}(|Du|^{p-2}Du + a(x,t)|Du|^{q-2}Du)=-\operatorname{div} (|F|^{p-2}F + a(x,t)|F|^{q-2}F) $$ in $Ω_T := Ω\times (0,T)\subset \mathbb{R}^n\times \mathbb{R}$, where $\frac{2n}{n+2}<p\leq 2$, $p<q$ and $0\leq a(\cdot)\in C^{α,\fracα{2}}(Ω_T)$. We establish gradient higher integrability results for weak solutions to the above problems under one of the following two assumptions: $$ u\in L^\infty (Ω_T) \quad\text{and}\quad q\leq p +\frac{α(p(n+2)-2n)}{4}, $$ or $$ u\in C(0,T;L^s(Ω)),\quad s\geq 2 \quad\text{and}\quad q\leq p+\frac{αμ_s}{n+s}, $$ where $μ_s := \frac{(p(n+2)-2n)s}{4}$. These results yield an interpolation refinement of gap bounds in the singular parabolic double phase setting.

math.AP↗
arXiv2026

Bounded solutions and interpolative gap bounds for degenerate parabolic double phase problems

We establish gradient higher integrability results for weak solutions to degenerate parabolic equations of double phase type $$ u_t-\operatorname{div} \left(|Du|^{p-2}Du + a(x,t)|Du|^{q-2}Du\right)=0 $$ in $Ω_T := Ω\times (0,T)$, where $a(\cdot)\in C^{α,\fracα{2}}(Ω_T)$. For bounded solutions, we prove that the result holds under the gap condition $$ q \leq p + α. $$ Moreover, for solutions with $$ u\in C(0,T;L^s(Ω)), \quad s \geq 2, $$ we obtain higher integrability under the gap condition $$ q \leq p + \frac{sα}{n+s}. $$ These results provide an interpolation between the gap bounds in the parabolic double phase setting.

math.AP↗
arXiv2026

Absence of the Lavrentiev phenomenon for degenerate parabolic double phase problems

We establish the absence of the Lavrentiev phenomenon for degenerate parabolic double phase problems. Any finite-energy function in the natural parabolic class admits smooth approximations with convergence in the parabolic Sobolev space and convergence of the corresponding energy. We provide explicit gap bound conditions and derive improved bounds under additional assumptions such as boundedness or stronger time regularity.

math.AP↗
arXiv2025

Parabolic Lipschitz truncation for multi-phase problems: the degenerate case

This article is devoted to exploring the Lipschitz truncation method for parabolic multi-phase problems. The method is based on Whitney decomposition and covering lemmas with a delicate comparison scheme of appropriate alternatives to distinguish phases, as introduced by the first and the second author in [24].

math.AP↗