Recovering First Order Integro-Differential Operators from Spectral Data [PDF]
arXiv, 2017 First order integro-differential operators on a finite interval are studied. Properties of spectral characteristic are established, and the uniqueness theorem is proved for the inverse problem of recovering operators from their spectral data.
arxiv
An analysis on the approximate controllability of neutral impulsive stochastic integrodifferential inclusions via resolvent operators. [PDF]
Heliyon, 2023 Ma YK +4 more
europepmc +1 more source
A priori bounds for degenerate and singular evolutionary partial integro-differential equations [PDF]
arXiv, 2010 We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these ...
arxiv
Estimates of the Green function for the fractional Laplacian perturbed by gradient [PDF]
arXiv, 2010 The Green function of the fractional Laplacian of the differential order bigger than one and the Green function of its gradient perturbations are comparable for bounded smooth multidimensional open sets if the drift function is in an appropriate Kato class.
arxiv
Comparability and regularity estimates for symmetric nonlocal Dirichlet forms [PDF]
arXiv, 2011 The aim of this work is to study comparability of nonlocal Dirichlet forms. We provide sufficient conditions on the kernel for local and global comparability. As an application we prove a-priori estimates in H\"{o}lder spaces for solutions to integrodifferential equations. These solutions are defined with the help of symmetric nonlocal Dirichlet forms.
arxiv
Principal eigenvalue of the fractional Laplacian with a large incompressible drift [PDF]
arXiv, 2013 We add a divergence-free drift with increasing magnitude to the fractional Laplacian on a bounded smooth domain, and discuss the behavior of the principal eigenvalue for the Dirichlet problem. The eigenvalue remains bounded if and only if the drift has non-trivial first integrals in the domain of the quadratic form of the fractional Laplacian.
arxiv
Regularity for anisotropic fully nonlinear integro-differential equations [PDF]
arXiv, 2013 We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We prove a nonlocal version of the ABP estimate, a Harnack inequality and the interior $C^{1, \gamma}$ regularity, extending the results of [Caffarelli and Silvestre, CPAM 62, 2009] to the anisotropic case.
arxiv
Constructions of free commutative integro-differential algebras [PDF]
Lect. Notes Computer Sci. 8372 (2014), 1-22, 2014 In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras by mixable shuffles. The first is by evaluations. The second is by the method of Gr\"obner-Shirshov bases.
arxiv
The Evans-Krylov theorem for nonlocal parabolic fully nonlinear equations [PDF]
arXiv, 2014 In this paper, we prove the Evans-Krylov theorem for nonlocal parabolic fully nonlinear equations.
arxiv
Hölder estimates for nonlocal-diffusion equations with drifts [PDF]
arXiv, 2014 We study a class of nonlocal-diffusion equations with drifts, and derive a priori $\Phi$-H\"older estimate for the solutions by using a purely probabilistic argument, where $\Phi$ is an intrinsic scaling function for the equation.
arxiv