To a nonlocal generalization of the Dirichlet problem

Abstract

A mixed problem with a boundary Dirichlet condition and nonlocal integral condition is considered for a two-dimensional elliptic equation.The existence and uniqueness of a weak solution of this problem are proved in a weighted Sobolev space.

Nonlinear Elliptic Equation With Nonlocal Integral Boundary Condition Depending on Two Parameters

“…The values of solution of two-dimensional problem (1.1)-(1.3) in one coordinate direction are conected by nonlocal condition (1.3). This is quite often and characteristic formulation of nonlocal condition for elliptic equation in two-or multi-dimensional case [1,2,3,4,5,13,14,18].…”

The Existence of a Generalized Solution of an m-Point Nonlocal Boundary Value Problem

“…In the work of J.R. Cannon [9], a nonlocal problem was posed, which initiated a new direction in the study of nonlocal boundary value problems and the problems of their numerical solution [1], [6], [25], [32]. In the work of A.V.…”

An Algorithm of the Solution of an Optimal Control Problem for Elliptic Equations

“…The Bitsadze-Samarski nonlocal boundary-value problem (see [3]) arose in connection with mathematical modeling of processes occurring in plasma physics. Extensive studies of Bitsadze-Samarski nonlocal problems (see [4]) and its various generalizations began in the 1980s [2][3][4][5]7].…”