A proof of the Cp′-regularity conjecture in the plane

Damião J. Araújo; Eduardo V. Teixeira; José Miguel Urbano

doi:10.1016/j.aim.2017.06.027

A proof of the Cp′-regularity conjecture in the plane

Damião J. Araújo, Eduardo V. Teixeira, José Miguel Urbano

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

30 Scopus citations

Abstract

We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class Cp′=C1, [Formula presented] this regularity is optimal.

Original language	English (US)
Pages (from-to)	541-553
Number of pages	13
Journal	Advances in Mathematics
Volume	316
DOIs	https://doi.org/10.1016/j.aim.2017.06.027
State	Published - Aug 20 2017
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2017.06.027

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AU - Araújo, Damião J.

AU - Teixeira, Eduardo V.

AU - Urbano, José Miguel

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PY - 2017/8/20

Y1 - 2017/8/20

N2 - We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class Cp′=C1, [Formula presented] this regularity is optimal.

AB - We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class Cp′=C1, [Formula presented] this regularity is optimal.

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SP - 541

EP - 553

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

A proof of the Cp′-regularity conjecture in the plane

Abstract

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