The smoothing property for a class of doubly nonlinear parabolic equations

Ebmeyer, Carsten; Urbano, José

doi:10.1090/S0002-9947-05-03790-6

The smoothing property for a class of doubly nonlinear parabolic equations
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by Carsten Ebmeyer and José Miguel Urbano PDF

Trans. Amer. Math. Soc. 357 (2005), 3239-3253 Request permission

Abstract:

We consider a class of doubly nonlinear parabolic equations used in modeling free boundaries with a finite speed of propagation. We prove that nonnegative weak solutions satisfy a smoothing property; this is a well-known feature in some particular cases such as the porous medium equation or the parabolic $p$-Laplace equation. The result is obtained via regularization and a comparison theorem.

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