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

By Damiao J. Ara'ujo, E. Teixeira, José Miguel Urbano. 2017

57 citations recorded by the source corpus.

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 C p ′ = C 1 , 1 p − 1 ; this regularity is optimal.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a2afdf78e6e49678594334ae0c63b3af686c2855

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Edgard A. Pimentel
2. G. Rampasso
3. Anne C. Bronzi
4. E. Teixeira

In Computational Theory and Mathematics

1. Edgard A. Pimentel
2. G. Rampasso
3. Anne C. Bronzi
4. E. Teixeira

Citations in the corpus

• Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, background): “We are ready to establish sharp geometric estimate at critical points of viscosity solutions to (2); compare it with the C ′ -regularity conjecture for functions whose p-laplacian are bounded, [9, 10].”