Citation: |
[1] |
L. Ambrosio, G. De Philippis and L. Martinazzi, $\Gamma$-convergence of nonlocal perimeter functionals, Manuscripta Math., 134 (2011), 377-403.doi: 10.1007/s00229-010-0399-4. |
[2] |
B. Barrios Barrera, A. Figalli and E. Valdinoci, Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), http://arxiv.org/abs/1202.4606v1. |
[3] |
L. Caffarelli, J.-M. Roquejoffre and O. Savin, Nonlocal minimal surfaces, Comm. Pure Appl. Math., 63 (2010), 1111-1144.doi: 10.1002/cpa.20331. |
[4] |
L. Caffarelli and P. E. Souganidis, Convergence of nonlocal threshold dynamics approximations to front propagation, Arch. Ration. Mech. Anal., 195 (2010), 1-23.doi: 10.1007/s00205-008-0181-x. |
[5] |
L. Caffarelli and E. Valdinoci, Uniform estimates and limiting arguments for nonlocal minimal surfaces, Calc. Var. Partial Differential Equations, 41 (2011), 203-240.doi: 10.1007/s00526-010-0359-6. |
[6] |
L. Caffarelli and E. Valdinoci, Regularity properties of nonlocal minimal surfaces via limiting arguments, Preprint, http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=11-69. |
[7] |
M. C. Caputo and N. Guillen, Regularity for non-local almost minimal boundaries and applications, Preprint, http://arxiv.org/abs/1003.2470. |
[8] |
E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. math., 136 (2012), 521-573.doi: 10.1016/j.bulsci.2011.12.004. |
[9] |
G. Franzina and E. Valdinoci, Geometric analysis of fractional phase transition interfaces, in "Geometric Properties for Parabolic and Elliptic PDE's" (Eds. A. Alvino, R. Magnanini and S. Sakaguchi), Springer INdAM Series, Springer-Verlag. http://cvgmt.sns.it/paper/1782/. |
[10] |
V. Maz'ya and T. Shaposhnikova, On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces, J. Funct. Anal., 195 (2002), 230-238.doi: 10.1006/jfan.2002.3955. |
[11] |
O. Savin and E. Valdinoci, Density estimates for a variational model driven by the Gagliardo norm, Preprint, http://arxiv.org/abs/1007.2114. |
[12] |
O. Savin and E. Valdinoci, $\Gamma$-convergence for nonlocal phase transitions, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), 479-500.doi: 10.1016/j.anihpc.2012.01.006. |
[13] |
O. Savin and E. Valdinoci, Regularity of nonlocal minimal cones in dimension $2$, Calc. Var. Partial Differential Equations, http://www.springerlink.com/content/467n313161531332. doi: 10.1007/s00526-012-0539-7. |
[14] |
A. Visintin, Nonconvex functionals related to multiphase systems, SIAM J. Math. Anal., 21 (1990), 1281-1304.doi: 10.1137/0521071. |
[15] |
A. Visintin, Generalized coarea formula and fractal sets, Japan J. Industrial Appl. Math., 8 (1991), 175-201.doi: 10.1007/BF03167679. |