This article is cited in 1 paper

On the existence of radially symmetric solutions for the $p$-Laplace equation with strong gradient nonlinearities

Ar. S. Tersenov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We consider the Dirichlet problem for the $p$-Laplace equation in presence of a gradient not satisfying the Bernstein–Nagumo type condition. We define some class of gradient nonlinearities, for which we prove the existence of a radially symmetric solution with a Hölder continuous derivative.

Keywords: $p$-Laplace equation, Bernstein–Nagumo condition, a priori estimates, radially symmetric solutions.

UDC: 517.95

MSC: 35R30

Received: 04.05.2023
Revised: 27.08.2023
Accepted: 25.09.2023

DOI: 10.33048/smzh.2023.64.616

 English version: Siberian Mathematical Journal, 2023, 64:6, 1443–1454