Hardy's inequality for functions vanishing on a part of the boundary

We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.Comment: 26 pages, 2 figures, includes several improvements in Sections 6-8 allowing to relax the assumptions in the main results. Final version published at http://link.springer.com/article/10.1007%2Fs11118-015-9463-

Perturbation of Δu+u(N+2)/(N−2)=0, the Scalar Curvature Problem in RN, and Related Topics

AbstractSome nonlinear elliptic equations on RN which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in RN are given

Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results

In this paper,we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero

Concentration of solutions for some singularly perturbed mixed problems. Part II: asymptotics of minimal energy solutions

In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the \uafrst paper [10]. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in [10]

Elliptic variational problems in R"N with critical growth

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal