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arXiv · 2012.07435

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

Sun-Sig Byun·Jeongmin Han
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Abstract

We study fully nonlinear parabolic equations in nondivergence form with oblique boundary conditions. An optimal and global Calder\'{o}n-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.

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Sun-Sig Byun, Jeongmin Han. 2020-12-14. $L^{p}$-estimates for the Hessians of solutions to fully nonlinear parabolic equations with oblique boundary conditions. https://arxiv.org/abs/2012.07435

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