Estimates near the boundary for solutions of second order parabolic equations.

Safonov, Mikhail

Displaying similar documents to “Estimates near the boundary for solutions of second order parabolic equations.”

Exact Schauder estimates of solutions of a boundary value problem for parabolic second order equations and their application to a nonlinear problem

Mikhail Borsuk (2002)

Annales Polonici Mathematici

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We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.

Morrey estimates for parabolic nondivergence operators of Hörmander type

Sufang Tang, Pengcheng Niu (2010)

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New a priori estimates for nondiagonal strongly nonlinear parabolic systems

Arina Arkhipova (2008)

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We consider nondiagonal elliptic and parabolic systems of equations with quadratic nonlinearities in the gradient. We discuss a new description of regular points of solutions of such systems. For a class of strongly nonlinear parabolic systems, we estimate locally the Hölder norm of a solution. Instead of smallness of the oscillation, we assume local smallness of the Campanato seminorm of the solution under consideration. Theorems about quasireverse Hölder inequalities proved by the...

Some theorems on the estimate and existence of solutions of integro-differential equations of parabolic type

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Existence of a classical solution for linear parabolic systems of nondivergence form

Masashi Misawa (2004)

Commentationes Mathematicae Universitatis Carolinae

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We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.