The Brezis–Nirenberg type problem involving the square root of the Laplacian
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ambrosetti A., Rabinowitz P.: Dual variational methods in critical points theory and applications. J. Funct. Anal. 14, 349–381 (1973)
Applebaum D.: Lévy processes—from probability to finance and quantum groups. Not. Am. Math. Soc. 51, 1336–1347 (2004)
Berestycki H., Lions P.L.: Nonlinear scalar field equations I, II. Arch. Rational Mech. Anal. 82, 313–375 (1983)
Brezis H., Lieb E.: A relation between pointwise convergence of functions and convergence of functionals. Proc. Am. Math. Soc. 88, 486–490 (1983)
Brezis H., Nirenberg L.: Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Commun. Pure Appl. Math. 36, 437–477 (1983)
Cabre X., Solà-Morales J.: Layer solutions in a half-space for boundary reactions. Commun. Pure Appl. Math. 58, 1678–1732 (2005)
Cabre X., Tan J.: Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv. Math. 224, 2052–2093 (2010)
Caffarelli L., Mellet A.: Random homogenization of fractional obstacle problems. Netw. Heterog. Media 3, 523–554 (2008)
Caffarelli L., Salsa S., Silvestre L.: Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Invent. Math. 171, 425–461 (2008)
Caffarelli L., Silvestre L.: An extension problem related to the fractional Laplacian. Commun. Part. Differ. Equ. 32, 1245–1260 (2007)
Chipot M., Chlebik M., Fila M., Shafrir I.: Existence of positive solutions of a semilinear elliptic equation in $${\mathbb R_{+}^{n}}$$ with a nonlinear boundary condition. J. Math. Anal. Appl. 223, 429–471 (1998)
Davila, J.: Singular Solutions of Semi-Linear Elliptic Problems. Handbook in Differential Equations: Stationary Partial Differential Equations, vol. 6, Chap. 2. Elsevier Science (2009)
Davila J., Dupaigne L.: The extremal solution of a boundary reaction problem. Commun. Pure Appl. Anal. 7, 795–817 (2008)
Evans, L.C.: Partial Differential Equations. Graduate Studies in Mathematics, vol. 19. AMS (1998)
Lions P.L.: The concentration-compactness principle in the calculus of variations. The limit case II. Rev. Mat. Iberoamericana 1, 45–121 (1985)
Lions, J.L., Magenes, E.: Non-homogeneous Boundary Value Problems and Applications, vol. I. Die Grundlehren der math. Wissenschaften 181, Springer-Verlag (1972)
Silvestre L.: Regularity of the obstacle problem for a fractional power of the Laplace operator. Commun. Pure Appl. Math. 60, 67–112 (2006)
Struwe M.: Variational Methods, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 34. Springer-Verlag, Berlin (1996)