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2014 A geometric tangential approach to sharp regularity for degenerate evolution equations
Eduardo Teixeira, José Urbano
Anal. PDE 7(3): 733-744 (2014). DOI: 10.2140/apde.2014.7.733

Abstract

That the weak solutions of degenerate parabolic PDEs modelled on the inhomogeneous p-Laplace equation

u t ÷ ( | u | p 2 u ) = f L q , r , p > 2

are C0,α, for some α(0,1), has been known for almost 30 years. What was hitherto missing from the literature was a precise and sharp knowledge of the Hölder exponent α in terms of p,q,r and the space dimension n. We show in this paper that

α = ( p q n ) r p q q [ ( p 1 ) r ( p 2 ) ]

using a method based on the notion of geometric tangential equations and the intrinsic scaling of the p-parabolic operator. The proofs are flexible enough to be of use in a number of other nonlinear evolution problems.

Citation

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Eduardo Teixeira. José Urbano. "A geometric tangential approach to sharp regularity for degenerate evolution equations." Anal. PDE 7 (3) 733 - 744, 2014. https://doi.org/10.2140/apde.2014.7.733

Information

Received: 12 August 2013; Revised: 20 January 2014; Accepted: 17 February 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1295.35296
MathSciNet: MR3227432
Digital Object Identifier: 10.2140/apde.2014.7.733

Subjects:
Primary: 35B65, 35K55, 35K65

Rights: Copyright © 2014 Mathematical Sciences Publishers

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