%0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 %D 2008 %T Transition layer for the heterogeneous Allen-Cahn equation %A Fethi Mahmoudi %A Andrea Malchiodi %A Juncheng Wei %X We consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$. %B Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 %G en_US %U http://hdl.handle.net/1963/2656 %1 1467 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-12T13:00:33Z\\nNo. of bitstreams: 1\\n0702878v1.pdf: 345060 bytes, checksum: a1e9182e6448c835b1c66b4f226b0b8d (MD5) %R 10.1016/j.anihpc.2007.03.008 %0 Journal Article %J J. Fixed Point Theory Appl. 1 (2007) 305-336 %D 2007 %T Boundary interface for the Allen-Cahn equation %A Andrea Malchiodi %A Juncheng Wei %B J. Fixed Point Theory Appl. 1 (2007) 305-336 %G en_US %U http://hdl.handle.net/1963/2027 %1 2169 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T11:10:26Z\\nNo. of bitstreams: 1\\nMalchiodiWei07.pdf: 379788 bytes, checksum: 4c87f76e7db9858a9acfeca0a8ec75c1 (MD5) %R 10.1007/s11784-007-0016-7 %0 Journal Article %J Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 %D 2007 %T Boundary-clustered interfaces for the Allen–Cahn equation %A Andrea Malchiodi %A Wei-Ming Ni %A Juncheng Wei %B Pacific Journal of Mathematics 229 (2007), No. 2, 447–468 %I Mathematical Sciences Publishers %G en %U http://hdl.handle.net/1963/5089 %1 4905 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-17T13:19:29Z\\nNo. of bitstreams: 1\\nmnw-pjm-final.pdf: 287316 bytes, checksum: 2a18e3af66be7b9b793a528138cf493a (MD5) %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 %D 2005 %T Multiple clustered layer solutions for semilinear Neumann problems on a ball %A Andrea Malchiodi %A Wei-Ming Ni %A Juncheng Wei %B Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 143-163 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3532 %1 732 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-20T10:15:49Z\\nNo. of bitstreams: 1\\nMalchiodiNiWei04.pdf: 340366 bytes, checksum: a0bb6df9ca59c557fdacb5e7142ecf3d (MD5) %R 10.1016/j.anihpc.2004.05.003