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- Title
- Boundary regularity for viscosity solutions of fully nonlinear degenerate/singular parabolic equations
- KIAS Author
- Yun, Hyungsung
- Journal
- CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2025
- Archive
-
- Abstract
- In this paper, we establish the boundary regularity results for viscosity solutions of fully nonlinear degenerate/singular parabolic equations of the form u(t )- x(n)(gamma) F(D(2)u, x, t) = f , where gamma < 1. These equations are motivated by the porous media type or fast diffusion type equations. We show the boundary C1,alpha-regularity of functions in their solutions class and the boundary C-2,C-alpha-regularity of viscosity solutions. As an application, we derive the global regularity results and the solvability of the Cauchy-Dirichlet problems