%0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 %D 2010 %T Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions %A Jesus Garcia Azorero %A Andrea Malchiodi %A Luigi Montoro %A Ireneo Peral %X 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 first paper. 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. %B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 %G en_US %U http://hdl.handle.net/1963/3409 %1 926 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-08T11:10:32Z\\nNo. of bitstreams: 1\\nGMMPII.pdf: 324708 bytes, checksum: 4829f5449fac58672d6e7a8e42efb3c4 (MD5) %R 10.1016/j.anihpc.2009.06.005 %0 Journal Article %J Arch. Ration. Mech. Anal. 196 (2010) 907-950 %D 2010 %T Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results %A Jesus Garcia Azorero %A Andrea Malchiodi %A Luigi Montoro %A Ireneo Peral %X 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. %B Arch. Ration. Mech. Anal. 196 (2010) 907-950 %G en_US %U http://hdl.handle.net/1963/3406 %1 927 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-08T11:03:36Z\\nNo. of bitstreams: 1\\nGMMPI.pdf: 466523 bytes, checksum: 004f66da4f9e531a535780337f19e185 (MD5) %R 10.1007/s00205-009-0259-0