Sharp regularity estimates for second order fully nonlinear parabolic equations
We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form (Formula Presented.)where F is elliptic with respect to the Hessian argument and f∈ Lp , q(Q1). The quantity Ξ(n,p,q):=np+2q determines to which regularity regime a solution of (Eq) belongs...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00255831_v369_n3-4_p1623_daSilva |
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| Sumario: | We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form (Formula Presented.)where F is elliptic with respect to the Hessian argument and f∈ Lp , q(Q1). The quantity Ξ(n,p,q):=np+2q determines to which regularity regime a solution of (Eq) belongs. We prove that when 1 < Ξ (n, p, q) < 2 - ϵF, solutions are parabolically α-Hölder continuous for a sharp, quantitative exponent 0 < α(n, p, q) < 1. Precisely at the critical borderline case, Ξ (n, p, q) = 1 , we obtain sharp parabolic Log-Lipschitz regularity estimates. When 0 < Ξ (n, p, q) < 1 , solutions are locally of class C1+σ,1+σ2 and in the limiting case Ξ (n, p, q) = 0 , we show parabolic C1 , Log-Lip regularity estimates provided F has “better” a priori estimates. © 2016, Springer-Verlag Berlin Heidelberg. |
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