A Harnack inequality for solutions of difference differential equations of elliptic-parabolic type.
Existence for a Cauchy-Dirichlet problem for evolutional p-Laplacian systems
We study the existence of a weak solution to a Cauchy-Dirichlet problem for evolutional p-Laplacian systems with constant coefficients and principal term only. The initial-boundary data is assumed to be a bounded weak solution of an evolutional p-Laplacian system with an L¹-function as external force. The key ingredient is the maximum principle for weak solutions.
Existence of a classical solution for linear parabolic systems of nondivergence form
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.
Existence and regularity results for the gradient flow for -harmonic maps.
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