Holder estimates for solutions of integra-differential equations like the fractional laplace

By Luis Silvestre. 2006

330 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8b4c85d862ccb5c1317caa820b7d606f699f0eb7

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Citations in the corpus

Symmetric jump processes and their heat kernel estimates (2009, background): “During the past several years there are also many interests from the theory of PDE (such as singular obstacle problems) to study non-local operators; see, for example, [10, 34] and the references therein.”
A nonlocal p-Laplacian evolution equation with Neumann boundary conditions (2008, methodology): “TOLEDO and variations of it, have been recently widely used to model diffusion processes, see [7], [8], [10], [17], [18], [19], [21], [25], [26], [29], [31] and [34].”
The weak Harnack inequality for the Boltzmann equation without cut-off (2016, neutral): “There are also many important results in this direction including [17], [60], [16], [15], [57], [22], [58], [13], [12], [19], [23], [25], [47], [26], [42] and [56].”
Dirichlet heat kernel estimates for rotationally symmetric Lévy processes (2013, background): “Recently, quite a few people in PDE are interested in problems related to non-local operators; see, for example, [5, 6, 7, 24] and the references therein.”
Weighted Poincaré inequality and heat kernel estimates for finite range jump processes (2008, background): “Recently there are also many interests from the theory of PDE (such as singular obstacle problems) to study non-local operators; see, for example, [7,31] and the references therein.”
Regularity for solutions of nonlocal, nonsymmetric equations (2012, methodology): “For nonlocal operators, point estimates were already given in [8].”
Regularity theory for fully nonlinear integro‐differential equations (2007, result): “1 using the ideas from [10].”
Decay estimates for nonlocal problems via energy methods (2009, background): “For recent references on nonlocal difiusion see [1]-[9], [11], [13]-[22], [ 26 ] and references therein.”
Regularity Results for Nonlocal Equations by Approximation (2009, background): “In [9], there is a very simple proof that solutions of integro-differential equations with variable order are Hölder continuous, as long as the order of the equation stays strictly away from 0 and 2.”
Delaunay-type singular solutions for the fractional Yamabe problem (2015, background): “This kind of kernels corresponds to tempered stable process and they have been studied in [20] and [32], for instance.”
Hölder regularity for nonlocal double phase equations (2019, methodology): “3 in [36] and Lemma 1 in [26].”
Localization of nonlocal gradients in various topologies (2015, background): “Various nonlocal operators have also been used implicitly in a number of works such as [5, 6], [8, 9, 25], [13, 14], and [3], for example.”
Hölder regularity for weak solutions to nonlocal double phase problems (2021, background): “We refer to, for instance, [7, 25, 26, 31, 39, 40, 41, 42, 44] for regularity results for nonlocal linear equations with fractional orders.”
Large solutions to elliptic equations involving fractional Laplacian (2013, background): “During the last years there has been a renewed and increasing interest in the study of linear and nonlinear integral operators, especially, the fractional Laplacian, motivated by great applications and by important advances on the theory of nonlinear partial differential equations, see [4, 6, 7, 9, ”