We consider divergence structure quasilinear singular elliptic partial differential equations on domains of R^n, and show that there exist solutions with dead cores, and even more, solutions which involve both a dead core and bursts within the core. The results are obtained under appropriate monotonicity conditions on both the nonlinearity and the elliptic operator. Important special cases treated here are the p-Laplace and the mean curvature operators. We also study related problems for p-Laplace equations with weights, which include the Matukuma equation as a prototype. While it is usually thought that dead cores arise due to loss of smoothness of the underlying equation, we show by examples that they can occur equally for analytic p-Laplace equations.
Dead Cores and Bursts for Quasilinear Singular Elliptic Equations
PUCCI, Patrizia;
2006
Abstract
We consider divergence structure quasilinear singular elliptic partial differential equations on domains of R^n, and show that there exist solutions with dead cores, and even more, solutions which involve both a dead core and bursts within the core. The results are obtained under appropriate monotonicity conditions on both the nonlinearity and the elliptic operator. Important special cases treated here are the p-Laplace and the mean curvature operators. We also study related problems for p-Laplace equations with weights, which include the Matukuma equation as a prototype. While it is usually thought that dead cores arise due to loss of smoothness of the underlying equation, we show by examples that they can occur equally for analytic p-Laplace equations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
