The estimates of the solution of the dirichlet problem with boundary function from Lp for a second-order elliptic equation

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki

Anatolii K Gushchin¹ 

[1] Steklov Mathematical Institute, Russian Academy of Sciences;

关键词: эллиптическое уравнение;    задача дирихле;    функциональное пространство;   

DOI  :  

来源: DOAJ

【 摘 要 】

We study the solvability of the Dirichlet problem for a second-order elliptic equation with measurable and bounded coefficients. Assuming that coefficients of equation are Dini-continued on the boundary, it is established that there is the unique solution of the Dirichlet problem with boundary function from $L_p$, $p > 1$. We prove the estimate of the analogue of area integral.

【 授权许可】

Unknown