Least supersolution approach to regularizing elliptic free boundary problems

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Title: Least supersolution approach to regularizing elliptic free boundary problems
Author: Moreira, Diego Ribeiro, 1977-
Abstract: In this dissertation , we study a free boundary problem obtained as a limit as [epsilon omplies 0] to the following regularizing family of semilinear equations [Delta]u = [Beta subscript epsilon] (u )F ([gradient]u ) , where [Beta subscript epsilon] approximates the Dirac delta in the origin and F is a Lipschitz function bounded away from 0 and infinity . The least supersolution approach is used to construct solutions satisfying geometric properties of the level surfaces that are uniform . This allows to prove that the free boundary of the limit has the "right" weak geometry , in the measure theoretical sense . By the construction of some barriers with curvature , the classification of global profiles for the blow -up analysis is carried out and the limit function is proven to be a viscosity and pointwise solution (a .e ) to a free boundary problem . Finally , the free boundary is proven to be a C[superscript 1 , alpha] surface around H[superscript n -1] a .e . point .
URI: http : / /hdl .handle .net /2152 /3374
Date: 2008-08-28

Citation

Least supersolution approach to regularizing elliptic free boundary problems. Doctoral dissertation, The University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /3374 .

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