Abstract and Applied Analysis (Jan 2000)

Solvability of quasilinear elliptic equations with strong dependence on the gradient

  • Darko Žubrinić

DOI
https://doi.org/10.1155/s1085337500000324
Journal volume & issue
Vol. 5, no. 3
pp. 159 – 173

Abstract

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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.