`a`
Communications on Pure and Applied Analysis (CPAA)
 

Layer solutions for an Allen-Cahn type system driven by the fractional Laplacian
Pages: 947 - 964, Issue 3, May 2016

doi:10.3934/cpaa.2016.15.947      Abstract        References        Full text (439.7K)           Related Articles

Yan Hu - College of Mathematics and Econometrics, Hunan University, Changsha 410082, China (email)

1 S. Alama, L. Bronsard and C. Gui, Stationary layered solutions in $\R^{2}$ for an Allen-Cahn system with multiple well potential, Calculus of Variations and Partial Differential Equations, 5 (1997), 359-390.       
2 L. Bronsard, C. Gui and M. Schatzman, A three layered minimizer in $\R^{2}$ for a variational problem with a symmetric three well potential, Communications on Pure and Applied Mathematics, 49 (1996), 677-715.       
3 L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Communications in Partial Differential Equations, 32 (2007), 1245-1260.       
4 X. Cabré and J. Solá-Morales, Layer solutions in a half-space for boundary reactions, Communications on Pure and Applied Mathematics, 58 (2005), 1678-1732.       
5 X. Cabré and Y. Sire, Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 31 (2014), 23-53.       
6 X. Cabré and Y. Sire, Nonlinear equations for fractional Laplacians II: existence, uniqueness, and qualitative properties of solutions, Transactions of the American Mathematical Society, 367 (2015), 911-941.       
7 X. Cabré and E. Cinti, Sharp energy estimates for nonlinear fractional diffusion equations, Calculus of Variations and Partial Differential Equations, 49 (2014), 233-269.       
8 X. Cabré and E. Cinti, Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian, Discrete and Continuous Dynamical System, 28 (2010), 1179-1206.       
9 E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bulletin des Sciences Mathématiques, 136 (2012), 521-573.       
10 E. B. Fabes, C. E. Kenig and R. P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Communications in Partial Differential Equations, 7 (1982), 77-116.       
11 G. Palatucci, O. Savin and E. Valdinoci, Local and global minimizers for a variational energy involving a fractional norm, Annali di Matematica Pura ed Applicata, 192 (2013), 673-718.       
12 L. Silvestre, Regularity of the obstacle problem for a fractional power of the Laplace operator, Communications on Pure and Applied Mathematics, 60 (2007), 67-112.       
13 Y. Sire and E. Valdinoci, Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result, Journal of Functional Analysis, 256 (2009), 1842-1864.       

Go to top