Sobolev inequality with non-uniformly degenerating gradient

被引：1

作者：

Mamedov, Farman ^{[1
]}

Monsurro, Sara ^{[2
]}

机构：

[1] Natl Acad Sci, Inst Math & Mech, B Vahabzade Str 9, AZ-1141 Baku, Azerbaijan

[2] Univ Salerno, Dept Math, Via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy

来源：

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2022年 / 24期

关键词：

Sobolev's inequality; homogeneous space; non-uniformly degenerating gradient; POINCARE INEQUALITIES; WEIGHTED SOBOLEV; VECTOR-FIELDS; ELLIPTIC-EQUATIONS; LOCAL REGULARITY; SPACES; GRUSHIN; THEOREMS; OPERATOR;

D O I：

10.14232/ejqtde.2022.1.24

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the following weighted Sobolev inequality in a bounded domain Omega subset of R-n, n >= 1, of a homogeneous space (R-n,p,wdx), under suitable compatibility conditions on the positive weight functions (v, w, w(1), w(2), ...,w(n)) and on the quasi-metric rho, (integral(Omega) vertical bar f vertical bar(q)v wdz)(1/q) <= C Sigma(N)(i=1) (integral(Omega)vertical bar f(zi)vertical bar(p)w(i)M(s)w dz)(1/p), f is an element of Lip(0)((Omega) over bar) where q >= p > 1 and Ms denotes the strong maximal operator. Some corollaries on non-uniformly degenerating gradient inequalities are derived.

引用

页码：1 / 19

页数：19

共 40 条

[1] WEIGHTED NORM INEQUALITIES FOR THE HARDY-LITTLEWOOD MAXIMAL OPERATOR ON SPACES OF HOMOGENEOUS TYPE [J].

AIMAR, H ;

MACIAS, RA .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 91 (02) :213-216

[2] ELLIPTIC AND PARABOLIC BMO AND HARNACK INEQUALITY [J].

AIMAR, H .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 306 (01) :265-276

[3]

Amanov RA, 2008, MATH NOTES+, V83, P3, DOI [10.4213/mzm4334, 10.1134/S000143460801001X]

[4] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

BREZIS, H ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) :437-477

[5]

Campos-Ortega Jose A., 1985, EMBRYONIC DEV DROSOP

[6] WEIGHTED POINCARE AND SOBOLEV INEQUALITIES AND ESTIMATES FOR WEIGHTED PEANO MAXIMAL FUNCTIONS [J].

CHANILLO, S ;

WHEEDEN, RL .

AMERICAN JOURNAL OF MATHEMATICS, 1985, 107 (05) :1191-1226

[7] DE GIORGI-MOSER THEOREM FOR A CLASS OF DEGENERATE NON-UNIFORMLY ELLIPTIC-EQUATIONS [J].

CHIARENZA, F ;

RUSTICHINI, A ;

SERAPIONI, R .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1989, 14 (05) :635-662

[8]

Coifman R., 1971, LECT NOTES MATH, V242

[9] Hardy inequalities related to Grushin type operators [J].

D'Ambrosio, L .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (03) :725-734

[10] Nonlinear Liouville theorems for Grushin and Tricomi operators [J].

D'Ambrosio, L ;

Lucente, S .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 193 (02) :511-541

← 1 2 3 4 →