Stephen Pankavich, Nicholas Michalowski
Abstract:
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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