September/October 2013 A priori estimates for elliptic problems with a strongly singular gradient term and a general datum
Daniela Giachetti, Francesco Petitta, Sergio Segura de León
Differential Integral Equations 26(9/10): 913-948 (September/October 2013). DOI: 10.57262/die/1372858556

Abstract

In this paper we show approximation procedures for studying singular elliptic problems whose model is $$ \begin{cases} - \Delta u= b(u)|\nabla u|^2+f(x), & \text{in } \; \Omega;\\ u = 0, & \text{on } \; \partial \Omega; \end{cases} $$ where $b(u)$ is singular in the $u$-variable at $u=0$, and $f \in L^m (\Omega)$, with $m>\frac N2$, is a function that does not have a constant sign. We will give an overview of the landscape that occurs when different problems (classified according to the sign of $b(s)$) are considered. So, in each case and using different methods, we will obtain a priori estimates, prove the convergence of the approximate solutions, and show some regularity properties of the limit.

Citation

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Daniela Giachetti. Francesco Petitta. Sergio Segura de León. "A priori estimates for elliptic problems with a strongly singular gradient term and a general datum." Differential Integral Equations 26 (9/10) 913 - 948, September/October 2013. https://doi.org/10.57262/die/1372858556

Information

Published: September/October 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1299.35139
MathSciNet: MR3100071
Digital Object Identifier: 10.57262/die/1372858556

Subjects:
Primary: 35J25 , 35J75,

Rights: Copyright © 2013 Khayyam Publishing, Inc.

Vol.26 • No. 9/10 • September/October 2013
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