A geometric tangential approach to sharp regularity for degenerate evolution equations

are $C^{0, α}$ , for some $α \in (0, 1)$ , 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 = \frac{(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.

Keywords

degenerate parabolic equations, sharp Hölder regularity, tangential equations, intrinsic scaling

Mathematical Subject Classification 2010

Primary: 35K55, 35K65, 35B65

Milestones

Received: 12 August 2013

Revised: 20 January 2014

Accepted: 17 February 2014

Published: 18 June 2014

Authors

Eduardo V. Teixeira
Department of Mathematics Universidade Federal do Ceará Campus of Pici Bloco 914 60455–760 Fortaleza-CE Brazil

José Miguel Urbano
CMUC, Department of Mathematics University of Coimbra 3001–501 Coimbra Portugal

Vol. 7, No. 3, 2014

Eduardo V. Teixeira and José Miguel Urbano

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors