Boundary concentration phenomena for a singularly perturbed elliptic problem

By A. Malchiodi, Marcelo Montenegro. 2002

166 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/28685dceaf3fee985bfa44bfeae5748a7b79b9af

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Spherical semiclassical states of a critical frequency for Schrodinger equations with decaying potentials (2006, background): “We mention [7, 11, 12, 15, 16] for some related problems on solutions with multidimensional concentrations.”
From Constant mean Curvature Hypersurfaces to the Gradient Theory of Phase Transitions (2003, background): “1. In [ 14 ], A. Malchiodi and M. Montenegro have constructed solutions of”
Concentration on curves for nonlinear Schrödinger Equations (2007, background): “In [24, 25, 28, 35] resonancephenomenasimilar to the“ û G -effect” hasbeenfaced in relatedproblems.”
MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R2 (2010, methodology): “The method is based on an innite dimensional form of Lyapunov Schmidt reduction, conceptually related with the method in [7], see also [ 16 , 17] Entire Solutions to Schr odinger type equations have been recently built in [6] and [18].”
Multidimensional boundary layers for a singularly perturbed Neumann problem (2004, methodology): “In the general case, the above conjecture was first proved in [34] for the case n = 2 and k = 1, under the technical assumption p ≥ 2.”
Singularly Perturbed Elliptic Equations with Symmetry: Existence of Solutions Concentrating on Spheres, Part I (2003, methodology): “Remark 3.5. The preceding arguments can be adapted to produce boundarylayer solutions, as in [ 20 ].”
The toda system and multiple-end solutions of autonomous planar elliptic problems (2007, background): “We refer the reader to [2, 3, 7, 11, 12, 13, 16, 20, 21, 27, 29, 30, 39, 37, 38] and references therein.”
Foliations by constant mean curvature tubes (2003, unknown): “[7] A. Malchiodi and M. Montenegro, Boundary concentration phenomena for a singularly perturbed elliptic problem, Comm. Pure Appl.”
Some new entire solutions of semilinear elliptic equations on Rn (2009, background): “For problem (P"), in [ 43 ], [44] it has been proved that, given any n 2 N and any p > 1, there exist solutions concentrating at the whole boundary of › if " tends to zero along a suitable sequence "j, corresponding to k = n i 1. The result has been extended in [37], [41] for general k, and the limi”
Multiple clustered layer solutions for semilinear Neumann problems on a ball (2005, background): “In [ 19 ], Malchiodi and Montenegro proved that for n = 2 and f(u) = up,p 2, there”
Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains (2005, methodology): “This method has also been used in [ 28 ], [29].”
The Toda System and Clustering Interfaces in the Allen–Cahn equation (2008, background): “Single-higher dimensional concentration phenomena has been the subject in, among other works, [12,25,26].”