Non-local gradient dependent operators

By Clayton Bjorland, Luis Caffarelli, Alessio Figalli. 2012

133 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ef9bd02ddf4e49a37538f3c660919d5cb4f4f0df

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Equivalence of solutions to fractional p-Laplace type equations (2016, background): “This is the direction taken in [2], [1], and [5].”
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].”
Integro-Differential equations with nonlinear directional dependence (2014, background): “The Harnack inequality is also stated to hold in [7] for a class which contains Asec, which cannot be true by [8, Theorem 1 and Example of p.”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “Another approach in the form of nonlocal gradient dependent operators is taken by Bjorland-Caffarelli-Figalli in [35].”
The weak Harnack inequality for the Boltzmann equation without cut-off (2016, background): “It is only in [19], [42] and [56] that more singular kernels are considered.”
Regularity theory for general stable operators (2014, background): “1), or related ones, has been widely investigated; see the works by Bass, Kassmann, Schwab, Silvestre, Sztonyk, and Bogdan, among others [1, 23, 22, 3, 39, 21, 2, 37, 5, 6, 7, 9, 24].”
On a new class of fractional partial differential equations (2014, methodology): “s;s equation - while it is not clear the former has a direct analogy in the real interpolation setting, the latter has been dened as the operator associated to minimizing the Gagliardo seminorm, e.g. [4,11,22]. In the setting of interpolation, the real and complex method complement each other to pro”
Global H\"older regularity for the fractional $p$-Laplacian (2014, methodology): “In [3] the fully non-linear approach is used to study the non-local analogue of the p-Laplacian equation in non-divergence form ∆u+ (p− 2) ∇u |∇u| (2)u ∇u |∇u| = 0, arising from non-local ‘tug of war’ games.”
Higher Hölder regularity for the fractional p-Laplacian in the superquadratic case (2017, background): “In [5] and [6] an interesting connection to a nonlocal tug-of-war is found, while the operator introduced in [11] is connected to Lévy processes.”
The Dirichlet Problem for the fractional p-Laplacian evolution equation (2015, unknown): “1) and its stationary versions are [8, 16, 27, 39].”