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In this paper we prove the optimal $L^p$-solvability of nonlocal parabolic equation with spatial dependent and non-smooth kernels.
Stein E.M.: Singular integrals and differentiability properties of functions. Princeton, N.J., Princeton University Press, 1970
1970
Earlier work this paper cites.
Bergh J. and Löfström J.: Interpolation spaces. Grundlehren der math. Wissen., 223, Springer-Verlag,1976
1976
Earlier work this paper cites.
Triebel H.: Interpolation Theory, Function Spaces, Differential Operators. North-Holland Publishing Company, Amsterdam, 1978
1978
Earlier work this paper cites.
Pazy A.: Semigroups of linear operators and applications to partial differential equations. Applied Mathematics Sciences, vol.44, Springer-Verlag, 1983
1983
Earlier work this paper cites.
Komatsu T.: On the martingale problem for generators of stable processes with perturbations. Osaka J. Math. 21(1984),113-132
1984
Earlier work this paper cites.
Mikulevicius R. and Pragarauskas H.: On the Cauchy problem for certain integro-differential operators in Sobolev and Hölder spaces. Lithuanian Math. Journal, Vol.32, No.2, 1992
1992
Earlier work this paper cites.
Stein E.M.: Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press, 1993
1993
Cited alongside, same era.
Amann H.: Linear and quasilinear parabolic problems. Vol. I, Abstract linear theory. Monographs in Mathematics, Vol.89, Birkhäuser Boston, MA, 1995
1995
Cited alongside, same era.
Biler P., Funaki T., Woyczynski W.A.: Fractal Burgers equations. J. Diff. Equa., 148, 9-46(1998)
1998
Cited alongside, same era.
Sato, K.: Lévy processes and infinitely divisible distributions. Cambridge University Press, 1999
1999
Cited alongside, same era.
Applebaum D.: Lévy processes and stochastic calculus. Cambridge Studies in Advance Mathematics 93, Cambridge University Press, 2004
2004
Cited alongside, same era.
Gilboa G. and Osher S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul., 7(3):1005-1028, 2008
2008
Later among the works it cites.
Krylov N.V.: Lectures on Elliptic and Parabolic Equations in Sobolev Spaces. AMS, Graduate Studies in Mathematics, Vol. 96, 2008
2008
Later among the works it cites.
Caffarelli L. and Vasseur A.: Drift diffusion equations with fractional diffusion and the quasigeostrophic equation. Annals of Math., Vol. 171, No. 3, 1903-1930(2010)
2010
Later among the works it cites.
Barles G., Chasseigne E. and Imbert C.: Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations. J. Eur. Math. Soc., Vol.13, 1-26(2011)
2011
Later among the works it cites.
Caffarelli L., Chan C.H. and Vasseur A.: Regularity theory for nonlinear integral operators. J. Amer. Math. Soc. 24 (2011) 849-869
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Cited in the paper.
Zhang X.: Stochastic Differential Equations with Sobolev Drifts and Driven by α \alpha -stable Processes. Annales de l’Institut Henri Poincaré, Probabilit¨¦s et Statistiques, in press
Cited in the paper.
Cited in the paper.
Cited in the paper.
2011
Later among the works it cites.