Quasilinear Lane-Emden equations with absorption and measure data

被引：23

作者：

Bidaut-Veron, Marie-Francoise ^{[1
]}

Nguyen Quoc Hung ^{[1
]}

Veron, Laurent ^{[1
]}

机构：

[1] Univ Tours, Lab Math & Phys Theor, Tours, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2014年 / 102卷 / 02期

关键词：

Quasilinear elliptic equations; Wolff potential; Maximal functions; Borel measures; Lorentz spaces; Lorentz-Bessel capacities;

D O I：

10.1016/j.matpur.2013.11.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of solutions to the equation -Delta(p)u + g(x,u) = mu when g(x,.) is a nondecreasing function and mu a measure. We characterize the good measures, i.e. the ones for which the problem has a renormalized solution. We study particularly the cases where g(x, u) = vertical bar x vertical bar(-beta)vertical bar u vertical bar(q-1)u and g(x, u) = sgn(u) (e(tau vertical bar u vertical bar lambda) -1). The results state that a measure is good if it is absolutely continuous with respect to an appropriate Lorentz-Bessel capacities. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：315 / 337

页数：23

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