Ukrainian Mathematical Bulletin

Volume 3, Issue 1, 2006 pp. 1-30.

Regularity of a Weak Solution to the First Initial Boundary-value Problem for a Nonlinear Degenerate Parabolic Equation

Authors: Boris V. Bazaliy, Nikolai V. Krasnoschok
Author institution: Institute of Applied Mathematics and Mechanics of NAS of Ukraine 74 R. Luxemburg Str., 83114, Donetsk, Ukraine bazaliy@iamm.ac.donetsk.ua

Summary: We prove that a homogeneous Dirichlet problem for the quasilinear degenerate parabolic equation v_t=v^{1+s}v_{xx}, 0s1, has a classical solution in weight H\"older spaces. The proof is based on obtaining coercive estimates for the homogeneous Dirichlet problem for the model equation $u_t=x^{1+s}u_{xx}+f$ on the half-axis $x>0$ by using methods of the potential theory.

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