Regularity of solutions to a fractional elliptic problem with mixed Dirichlet–Neumann boundary data

References

[1] B. Abdellaoui, A. Dieb and E. Valdinoci, A nonlocal concave-convex problem with nonlocal mixed boundary data, Commun. Pure Appl. Anal. 17 (2018), no. 3, 1103–1120. 10.3934/cpaa.2018053Search in Google Scholar

[2] B. Barrios and M. Medina, Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A, https://doi.org/10.1017/prm.2018.77. 10.1017/prm.2018.77Search in Google Scholar

[3] C. Brändle, E. Colorado, A. de Pablo and U. Sánchez, A concave-convex elliptic problem involving the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A 143 (2013), no. 1, 39–71. 10.1017/S0308210511000175Search in Google Scholar

[4] X. Cabré and J. Tan, Positive solutions of nonlinear problems involving the square root of the Laplacian, Adv. Math. 224 (2010), no. 5, 2052–2093. 10.1016/j.aim.2010.01.025Search in Google Scholar

[5] L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007), no. 7–9, 1245–1260. 10.1080/03605300600987306Search in Google Scholar

[6] J. Carmona, E. Colorado, T. Leonori and A. Ortega, Semilinear fractional elliptic problems with mixed Dirichlet–Neumann boundary conditions, preprint (2019), https://arxiv.org/abs/1902.08925v1. 10.1515/fca-2020-0061Search in Google Scholar

[7] E. Colorado and A. Ortega, The Brezis–Nirenberg problem for the fractional Laplacian with mixed Dirichlet–Neumann boundary conditions, J. Math. Anal. Appl. 473 (2019), no. 2, 1002–1025. 10.1016/j.jmaa.2019.01.006Search in Google Scholar

[8] E. Colorado and I. Peral, Semilinear elliptic problems with mixed Dirichlet–Neumann boundary conditions, J. Funct. Anal. 199 (2003), no. 2, 468–507. 10.1016/S0022-1236(02)00101-5Search in Google Scholar

[9] S. Dipierro, X. Ros-Oton and E. Valdinoci, Nonlocal problems with Neumann boundary conditions, Rev. Mat. Iberoam. 33 (2017), no. 2, 377–416. 10.4171/RMI/942Search in Google Scholar

[10] E. B. Fabes, C. E. Kenig and R. P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), no. 1, 77–116. 10.1080/03605308208820218Search in Google Scholar

[11] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Pure Appl. Math. 88, Academic Press, New York, 1980. Search in Google Scholar

[12] J.-L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications. Vol. I, Grundlehren Math. Wiss. 181, Springer, New York, 1972, 10.1007/978-3-642-65217-2Search in Google Scholar

[13] G. Molica Bisci, V. D. Radulescu and R. Servadei, Variational Methods for Nonlocal Fractional Problems, Encyclopedia Math. Appl. 162, Cambridge University, Cambridge, 2016. 10.1017/CBO9781316282397Search in Google Scholar

[14] E. Shamir, Regularization of mixed second-order elliptic problems, Israel J. Math. 6 (1968), 150–168. 10.1007/BF02760180Search in Google Scholar

[15] G. Stampacchia, Problemi al contorno ellitici, con dati discontinui, dotati di soluzionie Hölderiane, Ann. Mat. Pura Appl. (4) 51 (1960), 1–37. 10.1007/BF02410941Search in Google Scholar