Teoria de regularidade para equaÃÃes elÃpticas totalmente nÃo lineares com potenciais singulares e problemas de fronteira livre assintÃticos / Fully nonlinear singularly perturbed elliptic equations and limiting free boundary problems

AUTOR(ES)
FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

05/11/2010

RESUMO

In this work we develop a fully nonlinear theory for singularly perturbed elliptic equations problems with high energy activation. We esta-blish uniform and optimal gradient estimates of solutions and prove that minimal solutions are non-degenerated. For problems governed by concave equations, we establish uniform weak geometric properties of approximating level surfaces. We also provide a thorough analysis of the free boundary problem obtained as a limit as the parameter term goes to zero. We find the precise jumping condition of limiting solutions through the phase transi-tion, which involves a subtle homogenization process of the governing fully nonlinear operator. In particular, for rotational invariant operators, $F(D^2u)$, we show the normal derivative of limiting function is constant along the interface. Smoothness properties of the free boundary are also addressed.

ASSUNTO(S)

differential equations mathematical analysis geometria equaÃÃes diferenciais anÃlise matemÃtica matematica geometry

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