Regularity theory for parabolic nonlinear integral operators

By Luis Caffarelli, C. Chan, Alexis Vasseur. 2011

199 citations recorded by the source corpus.

Received by the editors March 8, 2010 and, in revised form, August 2, 2010, October 26, 2010, and December 17, 2010. 2010 Mathematics Subject Classification. Primary 35B65, 45G05, 47G10.

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

View Paper: https://www.semanticscholar.org/paper/588aec7115d7883e21641b07e785ffaaa9a28b75

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Citations in the corpus

Nonlocal self-improving properties (2015, unknown): “We finally remark that, in recent times, there has been much attention to the regularity of solutions to nonlocal problems, especially in the basic case of kernels with measurable coefficients; see for instance [1, 3, 5, 7, 8, 14].”
Representation of solutions and large-time behavior for fully nonlocal diffusion equations (2015, background): “For the regularity theory of nonlocal equations in case α = 1 or β = 2, we refer to [11, 7, 22, 4, 5, 30, 2, 49, 48] and the references therein.”
Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes (2016, methodology): “Vasseur [14], we prove that the minimizers of Gs satisfy an improved fractional Caccioppoli inequality and therefore belong to a particular subset of W .”
The weak Harnack inequality for the Boltzmann equation without cut-off (2016, background): “Some results in this direction are [44], [14], [41], [29], [21], [34], [43] and [33].”
Hölder regularity for weak solutions to nonlocal double phase problems (2021, methodology): “Later, Caffarelli, Chan and Vasseur [5] applied De Giorgi’s approach to linear parabolic equations with fractional orders involving general kernels Ksp with p = 2, and proved Hölder continuity of weak solutions.”
Regularity results for nonlocal parabolic equations (2013, background): “Erdös and Yau [27] apply the ideas of [10] to discrete situations.”
Local Hölder continuity for fractional nonlocal equations with general growth (2021, unknown): “[3] L. Caffarelli, C. H. Chan, and A. Vasseur, Regularity theory for parabolic nonlinear integral operators, J. Amer.”
Edge Universality of Beta Ensembles (2013, methodology): “The proof of the Hölder continuity in [25] requires extending the De Giorgi-Nash-Moser type method of Caffarelli, Chan and Vasseur [11] to the singular coefficient case and providing a priori estimates such as rigidity and level repulsion.”
Local Regularity for Parabolic Nonlocal Operators (2012, background): “Our article differs from [7] with regard to these three aspects.”
A Parabolic Problem with a Fractional Time Derivative (2015, methodology): “By a change of variables and differentiating in space (see [1] for details) we obtain that Deθ is a solution to (1.”
Schauder estimates for solutions of linear parabolic integro-differential equations (2014, methodology): “c equations such as Ho¨lder estimates, Cordes-Nirenberg type estimates and EvansKrylov theorem were stablished. Regularity for parabolic integro-differential equations has been also studied, e.g., in [8, 9, 10, 13, 14, 23] and many others. In this paper, we prove optimal pointwise Schauder estimates”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “A number of ideas come from Caffarelli-Vasseur [69] and [66] with difficult modifications due to the degenerate nonlinearity.”