The impact of a lower order term in a Dirichlet problem with a singular nonlinearity

被引：13

作者：

Boccardo, Lucio ^{[1
]}

Croce, Gisella ^{[2
,3
,4
]}

机构：

[1] Sapienza Univ Roma, Ist Lombardo, Piazzale Aldo Moro 5, I-00185 Rome, Italy

[2] Normandie Univ, Le Havre, France

[3] ULH, LMAH, F-76600 Le Havre, France

[4] FR CNRS 3335, 25 Rue Philippe Lebon, F-76600 Le Havre, France

来源：

PORTUGALIAE MATHEMATICA | 2019年 / 76卷 / 3-4期

关键词：

Weak solution; approximating problems; strong maximum principle; Schauder's fixed point theorem; ELLIPTIC-EQUATIONS; W-0(1,1) SOLUTIONS;

D O I：

10.4171/PM/2041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the existence and regularity of solutions to the following Dirichlet problem {-div(a(x)vertical bar del u vertical bar(p-2)del u) + u vertical bar u vertical bar(r-1) = f(x)/u(theta) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega proving that the lower order term u vertical bar u vertical bar(r-1) has some regularizing effects on the solutions.

引用

页码：407 / 415

页数：9

共 17 条

[1]

[Anonymous], 1965, ANN I FOURIER, DOI DOI 10.5802/AIF.204

[2] NONLINEAR ELLIPTIC-EQUATIONS IN R(N) WITHOUT GROWTH RESTRICTIONS ON THE DATA [J].

BOCCARDO, L ;

GALLOUET, T ;

VAZQUEZ, JL .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 105 (02) :334-363

[3]

Boccardo L, 2014, PROG NONLINEAR DIFFE, V85, P135

[4] W01,1 solutions in some borderline cases of Calderon-Zygmund theory [J].

Boccardo, Lucio ;

Gallouet, Thierry .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (09) :2698-2714

[5] A semilinear problem with a W01,1 solution [J].

Boccardo, Lucio ;

Croce, Gisella ;

Orsina, Luigi .

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2012, 23 (02) :97-103

[6]

Boccardo L, 2012, MANUSCRIPTA MATH, V137, P419, DOI 10.1007/s00229-011-0473-6

[7] Semilinear elliptic equations with singular nonlinearities [J].

Boccardo, Lucio ;

Orsina, Luigi .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (3-4) :363-380

[8] SEMI-LINEAR SECOND-ORDER ELLIPTIC EQUATIONS IN L1 [J].

BREZIS, H ;

STRAUSS, WA .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1973, 25 (04) :565-590

[9] REGULARITY OF THE SOLUTIONS TO NONLINEAR ELLIPTIC-EQUATIONS WITH A LOWER-ORDER TERM [J].

CIRMI, GR .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 25 (06) :569-580

[10]

Croce G., 2007, Rend. Mat. Appl., V27, P299

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