Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems

2020/04/14 by Jacques Giacomoni, Deepak Kumar, Giacomoni, J. +3
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2004.06699

Abstract

This article deals with the study of the following singular quasilinear equation: (P) \ -Δ_pu -Δ_qu = f(x) u^-δ, ugt;0 in \Om; u=0 on \pa\Om, . where \Om is a bounded domain in ℝ^N with C² boundary \pa\Om, 1< q< p0 and f∈ L^∞_loc(\Om) is a non-negative function which behaves like \textnormaldist(x,\pa\Om)^-\ba, \ba≥ 0 near the boundary of \Om. We prove the existence of a weak solution in W^1,p_loc(\Om) and its behaviour near the boundary for \ba

Citations

• On a singular nonlinear elliptic boundary-value problem

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