Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order

By Richard F. Bass, M. Kassmann. 2005

151 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/cd29fc4cd1a0abc2ed2e0e2eecbe1cc50b66f0b4

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

The weak Harnack inequality for the Boltzmann equation without cut-off (2016, unknown): “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].”
A priori estimates for integro-differential operators with measurable kernels (2009, methodology): “See [14 ]a nd [ 4 ] for related results where probabilistic methods are applied.”
Heat kernel estimates for jump processes of mixed types on metric measure spaces (2007, background): “See also [3, 4, 5, 7, 8, 21, 22] for related Harnack inequalities, Hölder continuity of harmonic functions and the Feller property for non-local operators.”
Regularity theory for parabolic nonlinear integral operators (2011, unknown): “Along these lines, see Bass and Kassmann [3, 2] (see also [4]).”
Regularity for solutions of nonlocal, nonsymmetric equations (2012, background): “It is known from the previous work in [8] and [2] that the same result holds even when σ = τ .”
Mixed local and nonlocal elliptic operators: regularity and maximum principles (2020, background): “Though conceptually different, the problems related to mixed order equations are closely related in spirit to the ones of variable order equations (see [39, 8, 9, 47]), which have themselves concrete significance in applied sciences (see e.”
Non-local dirichlet forms and symmetric jump processes (2006, background): “Additionally, regularity of harmonic functions is considered for variable order, non-symmetric operators in [BK05b], [HuKa05].”
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].”