Free Access
Issue |
ESAIM: COCV
Volume 22, Number 3, July-September 2016
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Page(s) | 832 - 841 | |
DOI | https://doi.org/10.1051/cocv/2015032 | |
Published online | 06 June 2016 |
- B. Barrios, E. Colorado, A. de Pablo and U. Sánchez, On some critical problems for the fractional Laplacian operator. J. Differ. Equ. 252 (2012) 6133–6162. [CrossRef] [Google Scholar]
- M. Bonforte, Y. Sire and J.L. Vazquez, Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains. Preprint arXiv:1404.6195 (2014). [Google Scholar]
- H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Commun. Pure Appl. Math. 36 (1983) 437–477. [Google Scholar]
- X. Cabré and Y. Sire, Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 31 (2014) 23–53. [Google Scholar]
- L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian. Commun. Part. Differ. Equ. 32 (2007) 1245–1260. [Google Scholar]
- W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation. Commun. Pure Appl. Math. 59 (2006) 330–343. [CrossRef] [MathSciNet] [Google Scholar]
- E. Colorado, A. de Pablo and U. Sánchez, Perturbations of a critical fractional equation. Pacific J. Math. 271 (2014) 65–84. [CrossRef] [MathSciNet] [Google Scholar]
- A. Cotsiolis and N.K. Tavoularis, Best constants for Sobolev inequalities for higher order fractional derivatives. J. Math. Anal. Appl. 295 (2004) 225–236. [CrossRef] [MathSciNet] [Google Scholar]
- F. Gazzola, H.-C. Grunau and E. Mitidieri, Hardy inequalities with optimal constants and remainder terms. Trans. Amer. Math. Soc. 356 (2004) 2149–2168. [CrossRef] [MathSciNet] [Google Scholar]
- F. Gazzola, H.-C. Grunau and G. Sweers, Polyharmonic Boundary Value Problems. Vol. 1991 of Lect. Notes Math. Springer, Berlin (2010). [Google Scholar]
- Y. Ge, Sharp Sobolev inequalities in critical dimensions. Michigan Math. J. 51 (2003) 27–45. [CrossRef] [MathSciNet] [Google Scholar]
- I.W. Herbst, Spectral theory of the operator (p2 + m2)1 / 2 − Ze2/r. Commun. Math. Phys. 53 (1977) 285–294. [CrossRef] [Google Scholar]
- J.-L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications. Vol. I, translated from the French by P. Kenneth. Springer, New York (1972). [Google Scholar]
- E. Mitidieri, A simple approach to Hardy inequalities. Mat. Zametki 67 (2000) 563–572 (in Russian). English transl.: Math. Notes 67 (2000) 479–486. [CrossRef] [Google Scholar]
- R. Musina and A.I. Nazarov, On fractional Laplacians. Commun. Partial Differ. Equ. 39 (2014) 1780–1790. [Google Scholar]
- R. Musina and A.I. Nazarov, Non-critical dimensions for critical problems involving fractional Laplacians. Rev. Mat. Iberoamer. 32 (2016) 257–266. [CrossRef] [Google Scholar]
- R. Musina and A.I. Nazarov, On fractional Laplacians − 2. Preprint arXiv:1408.3568 (2014). [Google Scholar]
- R. Musina and A.I. Nazarov, On the Sobolev and Hardy constants for the fractional Navier Laplacian. Nonlin. Anal. 121 (2015) 123–129. [CrossRef] [Google Scholar]
- P. Pucci and J. Serrin, Critical exponents and critical dimensions for polyharmonic operators. J. Math. Pures Appl. (9) 69 (1990) 55–83. [Google Scholar]
- R. Servadei and E. Valdinoci, The Brezis-Nirenberg result for the fractional Laplacian. Trans. Amer. Math. Soc. 367 (2015) 67–102. [CrossRef] [MathSciNet] [Google Scholar]
- R. Servadei and E. Valdinoci, A Brezis-Nirenberg result for non-local critical equations in low dimension. Commun. Pure Appl. Anal. 12 (2013) 2445–2464. [CrossRef] [MathSciNet] [Google Scholar]
- P.R. Stinga and J.L. Torrea, Extension problem and Harnack’s inequality for some fractional operators. Commun. Partial Differ. Equ. 35 (2010) 2092–2122. [Google Scholar]
- J. Tan, The Brezis-Nirenberg type problem involving the square root of the Laplacian. Calc. Var. Partial Differ. Equ. 42 (2011) 21–41. [CrossRef] [Google Scholar]
- H. Triebel, Interpolation Theory, Function Spaces, Differential Operators. Deutscher Verlag Wissensch. Berlin (1978). [Google Scholar]
- R.C.A.M. Van der Vorst, Best constant for the embedding of the space into L2N/ (N − 4)(Ω). Differ. Integral Equ. 6 (1993) 259–276. [Google Scholar]
- D.R. Yafaev, On the theory of the discrete spectrum of the three-particle Schrödinger operator. Mat. Sbornik 94(136) (1974) 567–593 (Russian); English transl.: Math. USSR Sbornik 23 (1974) 535–559. [Google Scholar]
- D.R. Yafaev, Mathematical Scattering Theory: Analytic Theory, Vol. 158 of Math. Surv. Monogr. AMS (2010). [Google Scholar]
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