Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs

2024/06/05 by Ram Baran Verma, Verma, Ram Baran, Mohan Mallick +1
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2406.03481

Abstract

This article investigates the exceptional set of the boundary for the following problem: \beginaligned -(∂ u)/(∂ t) + M_λ,Λ⁺(D²u) + b(x,t)⋅ Du + c(x,t)u =0 \rmin ~ Ω_T, \endaligned We provide a sufficient condition on the exceptional set in terms of the bound of the Hausdorff measure of this boundary portion. This condition ensures that even if the boundary values are not nonnegative on this portion, the supersolution remains nonnegative.

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