The role of absorption terms in Dirichlet problems for the prescribed mean curvature equation

被引：0

作者：

Oliva, Francescantonio ^{[1
]}

Petitta, Francesco ^{[1
]}

de Leon, Sergio Segura ^{[2
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Via Scarpa 16, I-00161 Rome, Italy

[2] Univ Valencia, Dept Anal Matemat, Dr Moliner 50, Burjassot 46100, Valencia, Spain

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2024年 / 31卷 / 04期

关键词：

Prescribed mean curvature; Functions of bounded variation; Non-parametric minimal surfaces; Nonlinear elliptic equations; L-1-data; QUASI-LINEAR PROBLEM; 1-LAPLACIAN EQUATION; CAPILLARY EQUATION; SINGULAR SOLUTION; UNIQUENESS; EXISTENCE; SURFACES; BEHAVIOR;

D O I：

10.1007/s00030-024-00936-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study existence and uniqueness of solutions to Dirichlet problems as {g(u) - div (Du/root 1 + |Du|(2 )= f in Omega, u = 0 on partial derivative Omega, where Omega is an open bounded subset of R-N(N >= 2) with Lipschitz boundary, g : R -> R is a continuous function and f belongs to some Lebesgue space. In particular, under suitable saturation and sign assumptions, we explore the regularizing effect given by the absorption term g(u) in order to get solutions for data f merely belonging to L-1(Omega) and with no small-ness assumptions on the norm. We also prove a sharp boundedness result for data in L-N(Omega) as well as uniqueness if g is increasing.

引用

页数：30

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