Sharp regularity for the inhomogeneous porous medium equation

Damião J. Araújo; Anderson F. Maia; José Miguel Urbano

doi:10.1007/s11854-020-0081-z

Sharp regularity for the inhomogeneous porous medium equation

Damião J. Araújo, Anderson F. Maia, José Miguel Urbano

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We show that locally bounded solutions of the inhomogeneous porous medium equation (Formaula preseneted.) m>1 are locally Hölder continuous, with exponent (Formaula preseneted.) where α0 denotes the optimal Hölder exponent for solutions of the homogeneous case. The proof relies on an approximation lemma and geometric iteration in the appropriate intrinsic scaling.

Original language	English (US)
Pages (from-to)	395-407
Number of pages	13
Journal	Journal d'Analyse Mathematique
Volume	140
Issue number	2
DOIs	https://doi.org/10.1007/s11854-020-0081-z
State	Published - Mar 1 2020
Externally published	Yes

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10.1007/s11854-020-0081-z

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title = "Sharp regularity for the inhomogeneous porous medium equation",

abstract = "We show that locally bounded solutions of the inhomogeneous porous medium equation (Formaula preseneted.) m>1 are locally H{\"o}lder continuous, with exponent (Formaula preseneted.) where α0 denotes the optimal H{\"o}lder exponent for solutions of the homogeneous case. The proof relies on an approximation lemma and geometric iteration in the appropriate intrinsic scaling.",

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AU - Araújo, Damião J.

AU - Maia, Anderson F.

AU - Urbano, José Miguel

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PY - 2020/3/1

Y1 - 2020/3/1

N2 - We show that locally bounded solutions of the inhomogeneous porous medium equation (Formaula preseneted.) m>1 are locally Hölder continuous, with exponent (Formaula preseneted.) where α0 denotes the optimal Hölder exponent for solutions of the homogeneous case. The proof relies on an approximation lemma and geometric iteration in the appropriate intrinsic scaling.

AB - We show that locally bounded solutions of the inhomogeneous porous medium equation (Formaula preseneted.) m>1 are locally Hölder continuous, with exponent (Formaula preseneted.) where α0 denotes the optimal Hölder exponent for solutions of the homogeneous case. The proof relies on an approximation lemma and geometric iteration in the appropriate intrinsic scaling.

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JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

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ER -

Sharp regularity for the inhomogeneous porous medium equation

Abstract

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