Electron. J. Diff. Equ., Vol. 2015 (2015), No. 205, pp. 1-9.

A short proof of increased parabolic regularity

Stephen Pankavich, Nicholas Michalowski

We present a short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates and an inductive method, can be extended to prove analogous results for problems with time-dependent coefficients, advection-diffusion or reaction diffusion equations, and nonlinear PDEs even when other tools, such as semigroup methods or the use of explicit fundamental solutions, are unavailable.

Submitted January 14, 2015. Published August 10, 2015.
Math Subject Classifications: 35K14, 35K40, 35A05.
Key Words: Partial differential equations; uniformly parabolic; regularity; Fokker-Planck; diffusion.

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Stephen Pankavich
Department of Applied Mathematics and Statistics
Colorado School of Mines
Golden, CO 80401, USA
email: pankavic@mines.edu
Nicholas Michalowski
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003, USA
email: nmichalo@nmsu.edu

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