Colorado Heras, EduardoOrtega García, Alejandro2021-02-182021-05-152019-05-15Colorado, E., Ortega, A. (2019). The Brezis–Nirenberg problem for the fractional Laplacian with mixed Dirichlet–Neumann boundary conditions. Journal of Mathematical Analysis and Applications, 473(2), 1002–10250022-247Xhttps://hdl.handle.net/10016/31953In this work we study the existence of solutions to the critical Brezis-Nirenberg problem when one deals with the spectral fractional Laplace operator and mixed Dirichlet-Neumann boundary conditions, i.e., {(-Delta)(s)u = lambda u+u(2:-1), u > 0 in Omega, u = 0 on Sigma D; partial derivative u/partial derivative v = 0 on Sigma(N), where Omega C R-N is a regular bounded domain, 1/2 < s < 1, 2(s)(*); is the critical fractional Sobolev exponent, 0 <= lambda epsilon R, v is the outwards normal to partial derivative Omega, Sigma(D), Sigma(N) are smooth (N - 1)-dimensional submanifolds of partial derivative Omega such that Sigma(D) U Sigma(N) = partial derivative Omega , Sigma(D) boolean AND Sigma(N) = 0, and ED fl EAr = F is a smooth (N- 2)-dimensional submanifold of 812.24eng© 2019 ElsevierAtribución-NoComercial-SinDerivadas 3.0 EspañaFractional LaplacianMixed boundary conditionsCritical pointsCritical problemsSemilinear problemsresearch articleMatemáticashttps://doi.org/10.1016/j.jmaa.2019.01.006open access100221025Journal of Mathematical Analysis and Application473AR/0000023243