The Behavior of Bounded Solutions of Quasilinear Elliptic Equations on Manifolds

A. B. Ivanov

Centre for New Information Technologies, Moscow State University

Abstract: We consider the behavior of bounded solutions of quasilinear elliptic equations on a special class of Riemannian manifolds. We obtain sufficient conditions for the convergence of solutions to zero.

Keywords: quasilinear elliptic equation, Riemannian manifold, $p$-harmonic function, maximum principle, Minkowski's inequality, Harnack's inequality, capacity.

UDC: 517.9

Received: 18.06.2008

DOI: 10.4213/mzm5265

 English version: Mathematical Notes, 2009, 86:1, 53–64

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