68 research outputs found
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 Îu+u(N+2)/(Nâ2)=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
Nonlinear elliptic problems with superlinear reaction and parametric concave boundary condition
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