Abstract and Applied Analysis

Solvability of quasilinear elliptic equations with strong dependence on the gradient

Darko Žubrinić

Abstract

We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involving $p$-Laplacian in the ball. We allow simultaneous strong dependence of the right-hand side on both the unknown function and its gradient. The elliptic problem is studied by relating it to the corresponding singular ordinary integro-differential equation. Solvability range is obtained in the form of simple inequalities involving the coefficients describing the problem. We also study a posteriori regularity of solutions. An existence result is formulated for elliptic equations on arbitrary bounded domains in dependence of outer radius of domain.

Article information

Source
Abstr. Appl. Anal., Volume 5, Number 3 (2000), 159-173.

Dates
First available in Project Euclid: 10 April 2003

https://projecteuclid.org/euclid.aaa/1049999318

Digital Object Identifier
doi:10.1155/S1085337500000324

Mathematical Reviews number (MathSciNet)
MR1885553

Zentralblatt MATH identifier
1005.35043

Subjects
Primary: 35J60: Nonlinear elliptic equations 45J05

Citation

Žubrinić, Darko. Solvability of quasilinear elliptic equations with strong dependence on the gradient. Abstr. Appl. Anal. 5 (2000), no. 3, 159--173. doi:10.1155/S1085337500000324. https://projecteuclid.org/euclid.aaa/1049999318