Second order regularity of solutions of elliptic equations in divergence form with Sobolev coefficients

被引：0
作者：
Perelmuter, M. A. [1 ]
机构：
[1] SCAD Soft Ltd, 3a Osvity, UA-03037 Kyiv, Ukraine
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2025年
关键词：
Elliptic operators; Second order regularity; Weak solutions; PDES;
D O I：
10.1007/s10231-025-01569-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give L-p estimates for the second derivatives of weak solutions to the Dirichlet problem for equation div(A del u)=f in Omega subset of R-d with Sobolev coefficients. In particular, for f is an element of L-2(Omega)boolean AND L-s(Omega) ||Delta u||(2) <= { c(1)||f||(2)+c(2)||del A||(2)(q)||f||s, if 1<s<d/2,1/2=2/q+1/s-2/d c(1)||f||(2)+c(2)||del A||(2)(4)||f||s, if s>d/2.
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页数：7
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