This article is cited in 1 paper

Dirichlet Problem for a Class of Quasilinear Elliptic Equations

A. S. Tersenov


Abstract: In this paper, the Dirichlet problem for quasilinear elliptic equations is studied. New a priori estimates of the solution and its gradient are obtained. These estimates are derived without any assumptions on the smoothness of the coefficients and the right-hand side of the equation. Moreover, an arbitrary growth of the right-hand side with respect to the gradient of the solution is assumed. On the basis of the resulting estimates, existence theorems are proved.

UDC: 517.95

Received: 28.08.2002

DOI: 10.4213/mzm134

 English version: Mathematical Notes, 2004, 76:4, 546–557

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