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Teixeira, Jo\\~ao Vitor da Silva","submitted_at":"2016-01-22T18:47:00Z","abstract_excerpt":"We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form \\begin{equation}\\label{Meq}\\tag{Eq} u_t- F(D^2u, Du, X, t) = f(X,t) \\quad \\mbox{in} \\quad Q_1, \\end{equation} where $F$ is elliptic with respect to the Hessian argument and $f \\in L^{p,q}(Q_1)$. The quantity $\\kappa(n, p, q):=\\frac{n}{p}+\\frac{2}{q}$ determines to which regularity regime a solution of \\eqref{Meq} belongs. We prove that when $1< \\kappa(n,p,q) < 2-\\epsilon_F$, solutions are parabolic-H\\\"{o}lder continuous for a sharp, quantitative exponent $0< \\alpha(n,p,q) < 1$. 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Teixeira, Jo\\~ao Vitor da Silva","submitted_at":"2016-01-22T18:47:00Z","abstract_excerpt":"We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form \\begin{equation}\\label{Meq}\\tag{Eq} u_t- F(D^2u, Du, X, t) = f(X,t) \\quad \\mbox{in} \\quad Q_1, \\end{equation} where $F$ is elliptic with respect to the Hessian argument and $f \\in L^{p,q}(Q_1)$. The quantity $\\kappa(n, p, q):=\\frac{n}{p}+\\frac{2}{q}$ determines to which regularity regime a solution of \\eqref{Meq} belongs. We prove that when $1< \\kappa(n,p,q) < 2-\\epsilon_F$, solutions are parabolic-H\\\"{o}lder continuous for a sharp, quantitative exponent $0< \\alpha(n,p,q) < 1$. 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