Semiregular solutions of elliptic boundary-value problems with discontinuous nonlinearities of exponential growth

Author:

Pavlenko Vyacheslav Nikolaevich1,Potapov Dmitriy Konstantinovich2

Affiliation:

1. Chelyabinsk State University, Chelyabinsk, Russia

2. Saint Petersburg State University, St. Petersburg, Russia

Abstract

An elliptic boundary-value problem with discontinuous nonlinearity of exponential growth at infinity is investigated. The existence theorem for a weak semiregular solution of this problem is deduced by the variational method. The semiregularity of a solution means that its values are points of continuity of the nonlinearity with respect to the phase variable almost everywhere in the domain where the boundary-value problem is considered. The variational approach used is based on the concept of a quasipotential operator, unlike the traditional approach, which uses Clarke's generalized derivative. Bibliography: 29 titles.

Funder

Russian Foundation for Basic Research

Publisher

Steklov Mathematical Institute

Subject

Algebra and Number Theory

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