On the local behavior of local weak solutions to some singular anisotropic elliptic equations

被引：20

作者：

Ciani, Simone ^{[1
]}

Skrypnik, Igor I. ^{[2
]}

Vespri, Vincenzo ^{[3
]}

机构：

[1] Tech Univ Darmstadt, Dept Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

[2] Natl Acad Sci Ukraine, Inst Appl Math & Mech, Gen Batiouk Str 19, UA-84116 Sloviansk, Ukraine

[3] Univ Firenze, Dipartimento Matemat & Informat Ulisse Dini Viale, 67-a, I-50134 Florence, Italy

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2023年 / 12卷 / 01期

关键词：

anisotropic p-Laplacian; singular parabolic equations; Holder continuity; intrinsic scaling; expansion of positivity; intrinsic Harnack inequality; NONNEGATIVE SOLUTIONS; PARABOLIC EQUATIONS; HOLDER CONTINUITY; BOUNDEDNESS; SOBOLEV; REGULARITY;

D O I：

10.1515/anona-2022-0275

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind Sigma(s)(i=1)partial derivative(ii)u Sigma(N)(i=1s+1)partial derivative(i)(A(i)(x, u, del u)) = 0, x is an element of Omega subset of subset of R-N for 1 <= s <= (N -1), where each operator A(i) behaves directionally as the singular p-Laplacian, 1 < p < 2. Throughout a parabolic approach to expansion of positivity we obtain the interior Holder continuity and some integral and pointwise Harnack inequalities.

引用

页码：237 / 265

页数：29

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