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Shuhei Kitano

Publications and source records attributed to Shuhei Kitano.

6 recordsLinked to original sources
arXiv2026

Ellipsoidal Positivity Sets for Fractional Obstacle Problems with Quadratic Forcing

Let \(n\ge1\), \(0 0\), and let \(A\) be a positive definite symmetric matrix. We prove that the unique decaying viscosity solution of \[ \min\{u,\,(-\Delta)^s u-(c-\langle Ax,x\rangle)\}=0 \qquad\text{in }\mathbb R^n \] has the form \[ u(x)=K\max\{1-\langle Bx,x\rangle,0\}^{1+s} \] for some \(K>0\) and some positive definite symmetric matrix \(B\). In particular, its positivity set is an ellipsoid. For \(s=1/2\) and \(n\ge2\), this result, combined with the classification of Fern\'andez-Real and Yu, implies that cubic global thin obstacle solutions with nonempty bounded positivity set have ellipsoidal positivity sets. This proves the conjecture of Fern\'andez-Real and Yu in the nonempty bounded-positivity case.

math.AP↗
arXiv2026

On the Aleksandrov--Bakelman--Pucci estimates for the weighted $1$-Laplacian

We establish Aleksandrov--Bakelman--Pucci-type estimates for viscosity subsolutions of Poisson equations associated with the weighted $1$-Laplacian and, more generally, with fully nonlinear operators acting on the Hessian in directions orthogonal to the gradient. A key feature of the proof is that the quasiconcave envelope plays the role of the concave envelope in the classical ABP estimate.

math.AP↗
arXiv2023

Second order $L_p$ estimates for subsolutions of fully nonlinear equations

We obtain new $L_p$ estimates for subsolutions to fully nonlinear equations. Based on our $L_p$ estimates, we further study several topics such as the third and fourth order derivative estimates for concave fully nonlinear equations, critical exponents of $L_p$ estimates and maximum principles, and the existence and uniqueness of solutions to fully nonlinear equations on the torus with free terms in the $L_p$ spaces or in the space of Radon measures.

math.AP↗
arXiv2022

$ W^{\sigma,p}$ A Priori Estimates for Fully Nonlinear Integro-Differential Equations

$W^{\sigma,p}$ estimates are studied for a class of fully nonlinear integro-differential equations of order $\sigma$, which are analogues of $W^{2,p}$ estimates by Caffarelli. We also present Aleksandrov-Bakelman-Pucci maximum principles, which are improvements of estimates proved by Guillen-Schwab, depending only on $L^p$ norms of inhomogeneous terms.

math.AP↗
arXiv2022

ABP maximum principles for fully nonlinear integro-differential equations with unbounded inhomogeneous terms

Aleksandrov-Bakelman-Pucci maximum principles are studied for a class of fully nonlinear integro-differential equations of order $\sigma\in [2-\varepsilon_0,2)$, where $\varepsilon_0$ is a small constant depending only on given parameters. The goal of this paper is to improve an estimate of Guillen and Schwab (Arch. Ration. Mech. Anal., 206, 2012) in order to avoid the dependence on $L^\infty$ norm of %the to the estimate depending only on $L^n$ norm the inhomogeneous term.

math.AP↗