Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geometry, vol.11, issue.4, pp.573-598, 1976. ,
Non-linear elliptic equations on Riemannian manifolds with the Sobolev critical exponent, Topics in geometry, Progr. Nonlinear Differential Equations Appl, vol.20, pp.1-100, 1996. ,
Existence and bifurcation of solutions for an elliptic degenerate problem, J. Differential Equations, vol.134, issue.1, pp.1-25, 1997. ,
The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math, vol.47, issue.1, pp.47-92, 1994. ,
Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math, vol.36, pp.437-477, 1983. ,
First order interpolation inequalities with weights, Compositio Math, vol.53, issue.3, pp.259-275, 1984. ,
Concentration estimates and multiple solutions to elliptic problems at critical growth, Adv. Differential Equations, vol.7, pp.1257-1280, 2002. ,
Elliptic equations with critical Sobolev exponents in dimension 3, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.19, issue.2, pp.125-142, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00194426
, From one bubble to several bubbles: the low-dimensional case, J. Differential Geom, vol.63, issue.3, pp.399-473, 2003.
Stability of elliptic PDEs with respect to perturbations of the domain, J. Differential Equations, vol.255, issue.10, pp.3703-3718, 2013. ,
Blow-up theory for elliptic PDEs in Riemannian geometry, Mathematical Notes, vol.45, 2004. ,
Stability of the Poho?aev obstruction in dimension 3, J. Eur. Math. Soc. (JEMS), issue.5, pp.1117-1149, 2010. ,
Positive solutions of semilinear equations in cones, Tran. Amer. Math. Soc, vol.11, pp.191-201, 1992. ,
Almgren-type monotonicity methods for the classification of behaviour at corners of solutions to semilinear elliptic equations, Proc. Roy. Soc. Edinburgh Sect. A, vol.143, issue.5, pp.957-1019, 2013. ,
, Duality and Perturbation Methods in Critical Point Theory, Cambridge Tracts in Mathematics, 1993.
Multiplicity and stability of the Pohozaev obstruction for Hardy-Sobolev equations, 2018. ,
, Functional inequalities: new perspectives and new applications, Mathematical Surveys and Monographs, vol.187, 2013.
, Sobolev Critical Elliptic Equations with Boundary Singularities, vol.21, pp.767-793, 2004.
The effect of curvature on the best constant in the Hardy-Sobolev inequalities, Geom. Funct. Anal, vol.16, issue.6, pp.1201-1245, 2006. ,
, Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth, International Mathematics Research Papers, issue.2187, pp.1-86, 2006.
Hardy-Singular Boundary Mass and Sobolev-Critical Variational Problems, Analysis and PDE, vol.10, issue.5, pp.1017-1079, 2016. ,
, Sobolev inequalities for the Hardy-Schrödinger operator: extremals and critical dimensions, Bull. Math. Sci, vol.6, issue.1, pp.89-144, 2016.
Hardy Sobolev inequalities with singularities on non smooth boundary: Hardy constant and extremals. Part I: Influence of local geometry, Nonlinear Analysis, vol.182, pp.316-349, 2019. ,
, Hardy-Sobolev inequalities with singularities on non smooth boundary. Part 2: Influence of the global geometry in small dimensions, 2019.
The Role played by Space Dimensions in Elliptic Critical Problems, Jour. Diff. Eq, vol.156, p.407426, 1999. ,
The Yamabe Problem, Bull. A.M.S, vol.17, issue.1, pp.37-91, 1987. ,
Minimizing problems for the Hardy-Sobolev type inequality with the singularity on the boundary, Tohoku Math. J, issue.2, pp.79-103, 2012. ,
Yamabe type equations on three-dimensional Riemannian manifolds, Commun. Contemp. Math, vol.1, issue.1, pp.1-50, 1999. ,
Existence of minimizers for Schrödinger operators under domain perturbations with application to Hardy's inequality, Indiana Univ, Math. J, vol.54, issue.4, pp.1061-1074, 2005. ,
Existence et asymptotiques optimales des fonctions de Green des opérateurs elliptiques d'ordre deux (Existence and optimal asymptotics of the Green's functions of second-order elliptic operators, 2010. ,
, Green's function for a singular Hardy-type operator with boundary singularity, 2017.
Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom, vol.20, issue.2, pp.479-495, 1984. ,
Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math, vol.92, issue.1, pp.47-71, 1988. ,
Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities, Trans. Amer. Math. Soc, vol.357, issue.7, pp.2909-2938, 2005. ,
, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol.34, 2008.
, Vancouver, V6T 1Z2 Canada E-mail address: nassif@math
, E-mail address: saikat@math.iitb.ac.in, saikat.mazumdar@iitb.ac
,