Regularity estimates for elliptic nonlocal operators
By Bartłomiej Dyda, M. Kassmann. 2015
65 citations recorded by the source corpus.
We study weak solutions to nonlocal equations governed by integrodifferential operators. Solutions are defined with the help of symmetric nonlocal bilinear forms. Throughout this work, our main emphasis is on operators with general, possibly singular, measurable kernels. We obtain regularity results which are robust with respect to the differentiability order of the equation. Furthermore, we provide a general tool for the derivation of H\"{o}lder a-priori estimates from the weak Harnack inequality. This tool is applicable for several local and nonlocal, linear and nonlinear problems on metric spaces. Another aim of this work is to provide comparability results for nonlocal quadratic forms.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/8a9e1bd8d4a952457f91511eb782023b7168f64d
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In Applied Mathematics
- Russell W. Schwab
- Luis Silvestre
- C. Imbert
- M. Kassmann
- Xavier Ros-Oton
- Juan Luis V'azquez
- Matthieu Felsinger
- Enrico Valdinoci
Citations in the corpus
- The weak Harnack inequality for the Boltzmann equation without cut-off (2016, background): “There is an interesting conjecture mentioned in [33] which is related to our condition (1.”
- Local Regularity for Parabolic Nonlocal Operators (2012, background): “[15], [12], [8], [14] and recently for fully nonlinear nonlocal parabolic equations in [9].”
- Regularity results for nonlocal parabolic equations (2013, methodology): “We note that none of the constants in the proof of [25] depend ρ in the underlying set, B.”
- The Dirichlet problem for nonlocal operators (2013, background): “In [9] the comparability of the quadratic forms needed for Lemma 2.”