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Lubomira Softova

Publications and source records attributed to Lubomira Softova.

10 recordsLinked to original sources
arXiv2026

Nonlocal problems for Laplace equation in Bochner spaces

We study the Laplace equation posed in the unbounded rectangular domain $Π= I \times (0,\infty)$ with $I= (0,2π)$, and subject to nonlocal boundary conditions on $\partial Π$ in the trace sense. The analysis is carried out in the Bochner-Sobolev space $W^2_{p,1}(Π;X)$, associated with the Bochner space $L^{p,1}(Π;X)$, with $ p \in (1,\infty)$ and $X$ is a suitable Banach space. To solve the problem, we employ a generalized spectral method. In particular, we introduce the notion of $\otimes$-basis generated by tensor products and extend the classical scheme known from the scalar case to the present setting. Moreover, we prove that the system of root functions of the corresponding nonlocal spectral problem forms a $\otimes$-basis in $L^p(I;X)$.

math.AP↗
arXiv2026

Interior a priori estimate for higher order elliptic systems in Orlicz spaces

We investigate singular integral operators with variable Calderón--Zygmund kernels and their commutators with $VMO$ functions on Orlicz spaces. After revisiting the classical $L^p$ theory, we establish boundedness results in $L^Φ$ under the standard $Δ_2$ and $\nabla_2$ conditions on the Young function. The analysis combines decomposition techniques with weak-type estimates to derive the main operator bounds. As an application, these results provide a functional-analytic framework for establishing a priori estimates and proving the interior regularity of solutions to higher-order elliptic equations and systems with discontinuous coefficients.

math.AP↗
arXiv2025

Approximation of the Solutions to Quasilinear Parabolic Problems with Perturbed $VMO_x$ Coefficients

We consider the Cauchy-Dirichlet problem for second-order quasilinear non-divergence form operators of parabolic type. The data are Cara\-thé\-o\-dory functions, and the principal part is of $VMO_x$-type with respect to the variables $ (x,t).$ Assuming the existence of a strong solution $u_0,$ we apply the Implicit Function Theorem in a small domain of this solution to show that small bounded perturbations of the data, locally in time, lead to small perturbations of the solution $u_0$. Additionally, we apply the Newton Iteration Procedure to construct an approximating sequence converging to the solution $u_0$ in the corresponding Sobolev space.

math.AP↗
arXiv2023

Boundedness of the solutions of a kind of nonlinear parabolic systems

We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carathéodory maps having controlled growth with respect to the solution and the gradient and the data are in anisotropic Lebesgue spaces. Under these assumptions we obtain essential boundedness of the weak solutions.

math.AP↗
arXiv2020

Precise Morrey regularity of the weak solutions to a kind of quasilinear systems with discontinuous data

We consider the Dirichlet problem for a class of quasilinear elliptic systems in domain with irregular boundary. The principal part satisfies componentwise coercivity condition and the nonlinear terms are Carathéodory maps having Morrey regularity in $x$ and verifying controlled growth conditions with respect to the other variables. We have obtained boundedness of the weak solution to the problem that permits to apply an iteration procedure in order to find optimal Morrey regularity of its gradient.

math.AP↗
arXiv2019

Asymptotically regular operators in generalized Morrey spaces

We obtain Calderón-Zygmund type estimates in generalized Morrey spaces for nonlinear equations of $p$-Laplacian type. Our result is obtained under minimal regularity assumptions both on the operator and on the domain. This result allows us to study asymptotically regular operators. As a byproduct, we obtain also generalized Hölder regularity of the solutions under some minimal restrictions of the weight functions.

math.AP↗
arXiv2017

Boundedness of the solutions to nonlinear systems with Morrey data

We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by functions in Morrey spaces. We firstly prove essential boundedness of the weak solution and then obtain Morrey regularity of its gradient.

math.AP↗
arXiv2015

The Dirichlet problem in a class of generalized weighted spaces

We show continuity in generalized weighted Morrey spaces of sub-linear integral operators generated by some classical integral operators and commutators. The obtained estimates are used to study global regularity of the solution of the Dirichlet problem for linear uniformly elliptic operators with discontinuous data.

math.AP↗
arXiv2013

Parabolic oblique derivative problem in generalized Morrey spaces

We study the regularity of the solutions of the oblique derivative problem for linear uniformly parabolic equations with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized Morrey space than the strong solution belongs to the corresponding generalized Sobolev-Morrey space.

math.AP↗