Extension and trace for nonlocal operators

Adams, 2003, Sobolev Spaces

Baeumer, 2018, Space-time fractional Dirichlet problems, Math. Nachr., 291, 2516, 10.1002/mana.201700111

Barles, 2014, On Neumann type problems for nonlocal equations set in a half space, Trans. Am. Math. Soc., 366, 4873, 10.1090/S0002-9947-2014-06181-3

Blumenthal, 1968, Markov Processes and Potential Theory, vol. 29

Bogdan, 1997, The boundary Harnack principle for the fractional Laplacian, Stud. Math., 123, 43, 10.4064/sm-123-1-43-80

Bogdan, 1999, Representation of α-harmonic functions in Lipschitz domains, Hiroshima Math. J., 29, 227, 10.32917/hmj/1206125005

Bogdan, 1999, Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains, Stud. Math., 133, 53, 10.4064/sm-133-1-53-92

Bogdan, 2000, Potential theory of Schrödinger operator based on fractional Laplacian, Probab. Math. Stat., 20, 293

Bogdan, 2014, On Hardy spaces of local and nonlocal operators, Hiroshima Math. J., 44, 193, 10.32917/hmj/1408972907

Bogdan, 2014, Density and tails of unimodal convolution semigroups, J. Funct. Anal., 266, 3543, 10.1016/j.jfa.2014.01.007

Bogdan, 2014, Dirichlet heat kernel for unimodal Lévy processes, Stoch. Process. Appl., 124, 3612, 10.1016/j.spa.2014.06.001

Bogdan, 2015, Barriers, exit time and survival probability for unimodal Lévy processes, Probab. Theory Relat. Fields, 162, 155, 10.1007/s00440-014-0568-6

Bogdan, 2012, Estimates of the Green function for the fractional Laplacian perturbed by gradient, Potential Anal., 36, 455, 10.1007/s11118-011-9237-x

Bogdan, 2017, Lévy systems and moment formulas for mixed Poisson integrals, vol. 72, 139

Bogdan, 2007, Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian, Stud. Math., 181, 101, 10.4064/sm181-2-1

Caffarelli, 2010, Nonlocal minimal surfaces, Commun. Pure Appl. Math., 63, 1111, 10.1002/cpa.20331

Chen, 2009, On notions of harmonicity, Proc. Am. Math. Soc., 137, 3497, 10.1090/S0002-9939-09-09945-6

Chen, 2012, Symmetric Markov Processes, Time Change, and Boundary Theory, vol. 35

Chen, 2014, Dirichlet heat kernel estimates for rotationally symmetric Lévy processes, Proc. Lond. Math. Soc. (3), 109, 90, 10.1112/plms/pdt068

Chung, 1995, From Brownian Motion to Schrödinger's Equation, vol. 312

Dhara, 2016, On one extension theorem dealing with weighted Orlicz-Slobodetskii space. Analysis on Lipschitz subgraph and Lipschitz domain, Math. Inequal. Appl., 19, 451

Di Nezza, 2012, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., 136, 521, 10.1016/j.bulsci.2011.12.004

Ding, 1996, A proof of the trace theorem of Sobolev spaces on Lipschitz domains, Proc. Am. Math. Soc., 124, 591, 10.1090/S0002-9939-96-03132-2

Dipierro, 2017, Nonlocal problems with Neumann boundary conditions, Rev. Mat. Iberoam., 33, 377, 10.4171/rmi/942

Dłotko, 2015, Quasi-geostrophic equation in R2, J. Differ. Equ., 259, 531, 10.1016/j.jde.2015.02.022

Douglas, 1931, Solution of the problem of plateau, Trans. Am. Math. Soc., 33, 263, 10.1090/S0002-9947-1931-1501590-9

Dyda, 2018, Function spaces and extension results for nonlocal Dirichlet problems, J. Funct. Anal.

Dynkin, 1965, Markov Processes. Vols. I, II, Bände 121, 122

Evans, 2010, Partial Differential Equations, vol. 19

Felsinger, 2015, The Dirichlet problem for nonlocal operators, Math. Z., 279, 779, 10.1007/s00209-014-1394-3

Fiscella, 2015, Density properties for fractional Sobolev spaces, Ann. Acad. Sci. Fenn., Math., 40, 235, 10.5186/aasfm.2015.4009

Fukushima, 2011, Dirichlet Forms and Symmetric Markov Processes, vol. 19

Grzywny

Grzywny, 2018, Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes, Stoch. Process. Appl., 128, 1, 10.1016/j.spa.2017.04.004

Grzywny, 2018, Asymptotic behaviour and estimates of slowly varying convolution semigroups, Int. Math. Res. Not.

Kang, 2013, On estimates of Poisson kernels for symmetric Lévy processes, J. Korean Math. Soc., 50, 1009, 10.4134/JKMS.2013.50.5.1009

Khoshnevisan, 2016, From Lévy-Type Processes to Parabolic SPDEs, 10.1007/978-3-319-34120-0

Klimsiak, 2015, Renormalized solutions of semilinear equations involving measure data and operator corresponding to Dirichlet form, NoDEA Nonlinear Differ. Equ. Appl., 22, 1911, 10.1007/s00030-015-0350-1

Koskela, 2017, Traces of weighted function spaces: dyadic norms and Whitney extensions, Sci. China Math., 60, 1981, 10.1007/s11425-017-9148-6

Kulczycki, 2016, Gradient estimates of harmonic functions and transition densities for Lévy processes, Trans. Am. Math. Soc., 368, 281, 10.1090/tran/6333

Millot, 2018, Asymptotics for the fractional Allen–Cahn equation and stationary nonlocal minimal surfaces, Arch. Ration. Mech. Anal.

Pruitt, 1981, The growth of random walks and Lévy processes, Ann. Probab., 9, 948, 10.1214/aop/1176994266

Ros-Oton, 2016, Nonlocal elliptic equations in bounded domains: a survey, Publ. Mat., 60, 3, 10.5565/PUBLMAT_60116_01

Rutkowski, 2018, The Dirichlet problem for nonlocal Lévy-type operators, Publ. Mat., 62, 213, 10.5565/PUBLMAT6211811

Sato, 1999, Lévy Processes and Infinitely Divisible Distributions, vol. 68

Schilling, 2012, Bernstein Functions. Theory and Applications, vol. 37

Servadei, 2014, Weak and viscosity solutions of the fractional Laplace equation, Publ. Mat., 58, 133, 10.5565/PUBLMAT_58114_06

Silvestre, 2007, Regularity of the obstacle problem for a fractional power of the Laplace operator, Commun. Pure Appl. Math., 60, 67, 10.1002/cpa.20153

Sztonyk, 2000, On harmonic measure for Lévy processes, Probab. Math. Stat., 20, 383

Wu, 2002, Harmonic measures for symmetric stable processes, Stud. Math., 149, 281, 10.4064/sm149-3-5