Sharp regularity for general Poisson equations with borderline sources
By E. Teixeira. 2011
55 citations recorded by the source corpus.
This article concerns optimal estimates for non-homogeneous degenerate elliptic equation with source functions in borderline spaces of integrability. We deliver sharp H\"older continuity estimates for solutions to $p$-degenerate elliptic equations in rough media with sources in the weak Lebesgue space $L_\text{weak}^{\frac{n}{p} + \epsilon}$. For the borderline case, $f \in L_\text{weak}^{\frac{n}{p}}$, solutions may not be bounded; nevertheless we show that solutions have bounded mean oscillation, in particular John-Nirenberg's exponential integrability estimates can be employed. All the results presented in this paper are optimal. Our approach is based on powerful Caffarelli-type compactness methods and it can be employed in a number order situations.
View Paper: https://www.semanticscholar.org/paper/1bc782a7b233a98e7de84f365cf6c1d787346370
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
Citations in the corpus
- Regularity for quasilinear equations on degenerate singular sets (2012, methodology): “See also [16] for similar reasoning on sharp regularity theory for quasilinear Poisson equations.”
- A proof of the Cp′-regularity conjecture in the plane (2017, background): “d a C1 corrector ξ, with kξkC1 ≪ 1, such that u+ξ is p-harmonic. This will allow us to frame the Cp′ conjecture into the formalism of the so called geometric tangential analysis, e.g. [7], [2, 1] and [17, 18, 19, 20, 21, 22]. Here is the precise statement. Lemma3. Let u ∈ W1,p(B 1) be a weak solutio”