A short proof of increased parabolic regularity

A short proof of increased parabolic regularity

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We present a short proof of the increased regularity obtained by solutions to rusk 6.66rr 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 kaiser copy stands solutions, are unavailable.