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Initial-Oblique Derivative Problem for Nonlinear Parabolic Equations in High Dimensional Domains

Dechang Chen, Guochun Wen


In this paper, we discuss some initial-boundary value problems for nonlinear nondivergent parabolic equations of second order in high dimensional domains, where coefficients of equations are measurable in multiply connected domains. We focus on initial-oblique derivative problems. The estimates of solutions for the initial-boundary value problems are given, and then the solvability result is derived. The results in this paper are the development of the corresponding work in [1, 3, 4].


initial-oblique derivative problems, nonlinear parabolic equations, high dimensional domains.

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