L^p-estimates for the Hessians of solutions to fully nonlinear parabolic equations with oblique boundary conditions

2020/12/14 by Byun, Sun-Sig, Han, Jeongmin · 2 citations
#35K20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35K55 #Secondary: 35K10

paper · doi:10.48550/arxiv.2012.07435

Abstract

We study fully nonlinear parabolic equations in nondivergence form with oblique boundary conditions. An optimal and global Calderón-Zygmund estimate is obtained by proving that the Hessian of the viscosity solution to the oblique boundary problem is as integrable as the nonhomogeneous term in L^p spaces under minimal regularity requirement on the nonlinear operator, the boundary data and the boundary of the domain.

Cited by

• Weighted Orlicz-Sobolev and variable exponent Morrey regularity for fully nonlinear parabolic PDEs with oblique boundary conditions and applications
• Fully Nonlinear Evolution equations: From Critical Integrability to Schauder Estimates

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