arXiv subjects

Lubomira G. Softova

Publications and source records attributed to Lubomira G. Softova.

10 recordsLinked to original sources

arXiv2025

Non-homogeneous conormal derivative problem for quasilinear elliptic equations with Morrey data

A non-homogeneous conormal derivative problem is considered for quasilinear divergence form elliptic equations modeled on the $m$-Laplacian operator. The nonlinear terms are given by Carathéodory functions and satisfy controlled growth structure conditions with respect to the solution and its gradient, while their $x$-behaviour is controlled in terms of suitable Morrey spaces. Global essential boundedness is proved for the weak solutions, generalizing thus the classical $L^p$-result of Ladyzhenskaya and Ural'tseva to the framework of the Morrey scales.

math.AP↗

arXiv2025

Global solvability of the Laplace equation in weighted Sobolev spaces

We consider a non-local boundary value problem for the Laplace equation in unbounded studding the weak and strong solvability of that problem in the framework of the weighted Sobolev space $W^{1,p}_ν$, with a Muckenhoupt weight. We proved that if any weak solution belongs to the space $W_ν^{2,p}$, then it is also a strong solution and satisfies the corespding boundary conditions. It should be noted that such problems do not fit into the general theory of elliptic equations and require a special technique.

math.AP↗

arXiv2024

Higher order elliptic equations in weighted Banach spaces

We consider higher order linear, uniformly elliptic equations with non-smooth coefficients in Banach-Sobolev spaces generated by weighted general Banach Function Space (BFS). Supposing boundedness of the Hardy-Littlewood Maximal and Calderon-Zygmund singular operators in BFSs we obtain local solvability in the Sobolev-BFS and establish interior Schauder type a priori estimates for the. elliptic operator. These results will be used in order to obtain Fredholmness of the operator under consideration in weighted BFSs with suitable weight. In addition, we analyze some examples of weighted BFS that verify our assumptions and in which the corresponding Schauder type estimates and Fredholmness of the operator hold true.

math.AP↗

arXiv2020

Venttsel boundary value problems with discontinuous data

We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the base of the a priori estimates obtained, maximal regularity and strong solvability in Sobolev spaces are proved.

math.AP↗

arXiv2020

Boundedness of Solutions to a Class of Coercive Systems with Morrey Data

We prove global essential boundedness for the weak solutions of divergence form quasilinear systems. The principal part of the differential operator is componentwise coercive and supports controlled growths with respect to the solution and its gradient, while the lower order term exhibits componentwise controlled gradient growth. The x-behaviour of the nonlinearities is governed in terms of Morrey spaces.

math.AP↗

arXiv2013

Global gradient estimates in weighted Lebesgue spaces for parabolic operators

We deal with the regularity problem for linear, second order parabolic equations and systems in divergence form with measurable data over non-smooth domains, related to variational problems arising in the modeling of composite materials and in the mechanics of membranes and films of simple non-homogeneous materials which form a linear laminated medium. Assuming partial BMO smallness of the coefficients and Reifenberg flatness of the boundary of the underlying domain, we develop a Calderón--Zygmund type theory for such parabolic operators in the settings of the weighted Lebesgue spaces. As consequence of the main result, we get regularity in parabolic Morrey scales for the spatial gradient of the weak solutions to the problems considered.

math.AP↗

arXiv2012

Lp-integrability of the gradient of solutions to quasilinear systems with discontinuous coefficients

The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in Reifenberg-flat domain is considered. The lower order terms supposed to satisfy controlled growth conditions. It is obtained Lp-integrability with p>2 of the gradient of the solution where p depends explicitly on the data. An analogous result is obtained also for the Cauchy-Dirichlet problem for quasilinear parabolic systems.

math.AP↗

arXiv2012

Generalized Morrey regularity for parabolic equations with discontinuity data

We obtain continuity in generalized parabolic Morrey spaces of sublinear integrals generated by the parabolic Calderón-Zygmund operators and its commutator with $VMO$ functions. The obtained estimates are used to study global regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations with discontinuous coefficients.

math.AP↗

arXiv2004

A'priori estimates and precise regularity for parabolic systems with discontinuous data

We deal with linear parabolic (in sense of Petrovskii) systems of order 2b with discontinuous principal coefficients. A'priori estimates in Sobolev and Sobolev--Morrey spaces are proved for the strong solutions by means of potential analysis and boundedness of certain singular integral operators with kernels of mixed homogeneity. As a byproduct, precise characterization of the Morrey, BMO and Hölder regularity is given for the solutions and their derivatives up to order 2b-1. Some counterexamples of recent publications announcing estimates similar to the obtained here are also given.

math.AP↗

arXiv2003

W^{2,1}_p Solvability for Parabolic Poincare Problem

We study Poincaré problem for a linear uniformly parabolic operator $¶$ in a cylinder $Q=Ω\times (0,T).$ The boundary operator $\B$ is defined by an oblique derivative with respect to a tangential vector field $ł$ defined on the lateral boundary $S.$ The coefficients of $¶$ are supposed to be $VMO$ away from the set of tangency $E$ and to possess higher regularity in $x$ near to $E.$ A unique strong solvability result is obtained in $W^{2,1}_p(Q)$ for all $p\in (1,\infty).$

math.AP↗