On weak solutions of boundary value problems for some general differential equations

被引：0

作者：

Burskii, V. P. ^{[1
]}

机构：

[1] Natl Res Univ, Moscow Inst Phys & Technol, Dolgoprudnyi, Moscow Region, Russia

来源：

IZVESTIYA MATHEMATICS | 2023年 / 87卷 / 05期

关键词：

partial differential equation; general theory of boundary value problems; boundary value problem; well-posedness; weak solution;

D O I：

10.4213/im9403e

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study general settings of the Dirichlet problem, the Neumann problem, and other boundary value problems for equations and systems of the form L(+)ALu = f with general (matrix, generally speaking) differential operation L and some linear or non-linear operator A acting in L-2(k)(Omega)-spaces. For these boundary value problems, results on well-posedness, existence and uniqueness of a weak solution are obtained. As an operator A, we consider Nemytskii and integral operators. The case of operators involving lower-order derivatives is also studied.

引用

页码：891 / 905

页数：15

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