Estimates on elliptic equations that hold only where the gradient is large

By C. Imbert, Luis Silvestre. 2013

90 citations recorded by the source corpus.

We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Holder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6241ab47647e0066c6ceb5fa6745e6758497ff98

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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

In Mathematical Physics

1. E. Teixeira
2. Edgard A. Pimentel

Citations in the corpus

• Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, background): “Local Hölder continuity was proven independently in [21] and [25] by means of Alexandroff-Bakelman-Pucci estimate; see also [27] for a much more robust treatment.”