Isolated singularities of solutions to quasi-linear elliptic equations with absorption

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:338

Article

Liskevich, Vitali¹  Skrypnik, I. I.² 

[1] Univ Coll Swansea, Dept Math, Swansea SA2 8PP, W Glam, Wales

[2] Inst Appl Math & Mech, Donetsk, Ukraine

关键词: isolated singularities;    quasi-linear equations;    kato-type classes;   

DOI  :  10.1016/j.jmaa.2007.05.018

来源: Elsevier

【 摘 要 】

We study the problem of removability of isolated singularities for a general second-order quasi-linear equation in divergence form -divA(x, u, del u) + a(0)(x, u) + g(x, u) = 0 in a punctured domain Omega\{0}, where Omega is a domain in R-n, n >= 3. The model example is the equation -Delta(p)u + gu vertical bar u vertical bar(p-2) + u vertical bar u vertical bar(q-1) = 0, q > p-1 > 0, p < n. Assuming that the lower-order terms satisfy certain non-linear Kato-type conditions, we prove that for q >= n(p-1)/n-p all point singularities of the above equation are removable, thus extending the seminal result of Brezis and Veron. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free