arXiv subjects

L. G. Softova

Publications and source records attributed to L. G. Softova.

3 recordsLinked to original sources

arXiv2026

Conormal problem for a kind of nonlinear elliptic equations

We study the global boundedness of weak solutions to a class of nonlinear elliptic equations in bounded Lipschitz domains, subject to conormal boundary conditions. Using techniques from Morrey space theory, Adams--Mazya trace inequalities, and higher integrability properties of the gradient, we derive uniform a priori bounds for the solutions. A crucial step in our analysis is the construction of appropriate measures associated with the solution and the application of the Hartman--Stampacchia lemma, which enables us to control the solution up to the boundary of the domain.

math.AP↗

arXiv2023

Nonstationary Venttsel problems with discontinuous data

We study linear and quasilinear Venttsel initial-boundary value problems for parabolic operators with discontinuous coefficients. On the basis of the a priori estimates obtained, strong solvability in composite Sobolev spaces is proved.

math.AP↗

arXiv2002

Singular Integrals and Commutators in Generalized Morrey Spaces

The present paper deals with singular integrals with variable Caldero'n-Zygmund type kernels satisfying mixed homogeneity condition. The continuity of these operators in The Lebesgue spaces is well studied by Fabes and Rivie're. Our goal is to extend their results in generalized Morrey spaces with weight satisfying suitable dabbling and integral conditions. A special attention is paid also of the commutators of the kernel with functions of bounded or vanishing mean oscillation.

math.FA↗