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Asymptotics of the $s$-perimeter as $s\searrow 0$
1. | SISSA - International School for Advanced Studies, Sector of Mathematical Analysis Via Bonomea, 265, 34136 Trieste, Italy |
2. | University of Texas at Austin, Department of Mathematics, 2515 Speedway Stop C1200, Austin, TX 78712-1202 |
3. | Università degli Studi di Parma, Dipartimento di Matematica Campus - Parco Area delle Scienze, 53/A, 43124 Parma, Italy |
4. | Università degli Studi di Milano, Dipartimento di Matematica Via Saldini, 50, 20133 Milano |
References:
[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), ().
|
[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, (): 11.
|
[7] |
M. C. Caputo and N. Guillen, Regularity for non-local almost minimal boundaries and applications,, Preprint, ().
|
[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, ().
|
[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, ().
|
[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, ().
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. |
show all references
References:
[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), ().
|
[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, (): 11.
|
[7] |
M. C. Caputo and N. Guillen, Regularity for non-local almost minimal boundaries and applications,, Preprint, ().
|
[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, ().
|
[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, ().
|
[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, ().
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. |
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