Regularity up to the boundary for singularly perturbed fully nonlinear elliptic equations

2015/10/08 by Ricarte, Gleydson C., da Silva, João Vitor
#35B25 #35B65 #35D40 #35J15 #35J60 #35J75 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.02193

Abstract

In this article we are interested in studying regularity up to the boundary for one-phase singularly perturbed fully nonlinear elliptic problems, associated to high energy activation potentials, namely F(X, ∇ u^ε, D² u^ε) = ζ_ε(u^ε) in Ω⊂ \Rⁿ where ζ_ε behaves asymptotically as the Dirac measure δ₀ as ε goes to zero. We shall establish global gradient bounds independent of the parameter ε.

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