Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
暂无分享,去创建一个
J. L. Varona | L. Roncal | P. R. Stinga | J. Torrea | P. Stinga | L. Roncal | 'Oscar Ciaurri | 'O. Ciaurri | J. L. Torrea | Ó. Ciaurri | J. Varona
[1] E. Valdinoci,et al. Density estimates for a variational model driven by the Gagliardo norm , 2010, 1007.2114.
[2] P. R. Stinga,et al. Extension Problem and Harnack's Inequality for Some Fractional Operators , 2009, 0910.2569.
[3] Enrico Valdinoci,et al. Density Estimates for a Nonlocal Variational Model via the Sobolev Inequality , 2011, SIAM J. Math. Anal..
[4] F'elix del Teso,et al. Finite difference method for a fractional porous medium equation , 2013, 1301.4349.
[5] A. Gray. Bessel Functions , 1899, Nature.
[6] Heat Kernel Expansions on the Integers , 2002, math/0206089.
[7] J. Cooper. SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONS , 1973 .
[8] Luis Silvestre,et al. Regularity of the obstacle problem for a fractional power of the laplace operator , 2007 .
[9] L. Roncal,et al. Transference of Fractional Laplacian Regularity , 2014 .
[10] Teruo Ushijima,et al. A Note on the Fractional Powers of Operators Approximating a Positive Definite Selfadjoint Operator , 1993 .
[11] Juan Luis Varona,et al. On a connection between the discrete fractional Laplacian and superdiffusion , 2015, Appl. Math. Lett..
[12] Gabriel Acosta,et al. A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations , 2015, SIAM J. Numer. Anal..
[13] N. S. Landkof. Foundations of Modern Potential Theory , 1972 .
[14] P. R. Stinga,et al. Fractional elliptic equations, Caccioppoli estimates and regularity , 2014, 1409.7721.
[15] J. L. Varona,et al. Harmonic analysis associated with a discrete Laplacian , 2014, 1401.2091.
[16] M Kardar,et al. Fractional Laplacian in bounded domains. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.
[17] E. Stein,et al. Discrete analogues in harmonic analysis II: Fractional integration , 2000 .
[18] Ricardo H. Nochetto,et al. A PDE Approach to Fractional Diffusion in General Domains: A Priori Error Analysis , 2013, Found. Comput. Math..
[19] Pablo Raúl Stinga,et al. Fractional powers of second order partial differential operators: extension problem and regularity theory , 2010 .
[20] Kay L Kirkpatrick,et al. On the Continuum Limit for Discrete NLS with Long-Range Lattice Interactions , 2011, 1108.6136.
[21] E. Stein,et al. Introduction to Fourier Analysis on Euclidean Spaces. , 1971 .
[22] Pedro J. Miana,et al. Extension problem and fractional operators: semigroups and wave equations , 2012, 1207.7203.
[23] A. Laforgia,et al. On the asymptotic expansion of a ratio of gamma functions , 2012 .
[24] J. Klafter,et al. The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .
[25] L. Caffarelli,et al. An Extension Problem Related to the Fractional Laplacian , 2006, math/0608640.
[26] R. Getoor,et al. First passage times for symmetric stable processes in space , 1961 .
[27] Yu. A. Brychkov,et al. Integrals and series , 1992 .
[28] G. A. Watson. A treatise on the theory of Bessel functions , 1944 .
[29] L. Roncal,et al. Fractional Laplacian on the torus , 2012, 1209.6104.
[30] Joseph E. Pasciak,et al. Numerical approximation of fractional powers of elliptic operators , 2013, Math. Comput..
[31] Adam M. Oberman,et al. Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach , 2013, SIAM J. Numer. Anal..