Regularizing effect of absorption terms in singular problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Oliva, Francescantonio¹ 

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

关键词: Semilinear elliptic equations;    Singular elliptic equations;    Regularizing effects;    Regularizing terms;    1-Laplacian;   

DOI  :  10.1016/j.jmaa.2018.11.069

来源: Elsevier

【 摘 要 】

We prove existence of solutions to problems whose model is {-Delta(p)u + u(q) = f/u(gamma) in Omega, u >= 0 in Omega, u = 0 on partial derivative Omega, where Omega is an open bounded subset of R-N (N >= 2), Delta(p)u is the p-laplacian operator for 1 <= p < N, q > 0, gamma >= 0 and f is a nonnegative function in L-m(Omega) for some m >= 1. In particular we analyze the regularizing effect produced by the absorption term in order to infer the existence of finite energy solutions in case gamma <= 1. We also study uniqueness of these solutions as well as examples which show the optimality of the results. Finally, we find local W-1,W-P-solutions in case gamma > 1. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free