Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 5, Number 3 (2000), 159-173.
Solvability of quasilinear elliptic equations with strong dependence on the gradient
We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involving -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.
Abstr. Appl. Anal., Volume 5, Number 3 (2000), 159-173.
First available in Project Euclid: 10 April 2003
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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