A short proof of increased parabolic regularity
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/205/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |