Higher Order Gamma-limits for Singularly Perturbed Dirichlet--Neumann Problems
نویسندگان
چکیده
منابع مشابه
Higher Order Energy Expansions for Some Singularly Perturbed Neumann Problems
We consider the following singularly perturbed semilinear elliptic problem: 2 u ? u + u p = 0 in ; u > 0 in and @u @ = 0 on @; where is a bounded smooth domain in R N , > 0 is a small constant and p is a sub-critical exponent. Let J u] := R (2 2 jruj 2 + 1 2 u 2 ? 1 p+1 u p+1)dx be its energy functional, where u 2 H 1 ((). Ni and Takagi ((15], 16]) proved that for a single boundary spike soluti...
متن کاملSingularly perturbed Neumann problems with potentials
Such a problem was intensively studied in several works. For example, Ni & Takagi, in [11, 12], show that, for ε sufficiently small, there exists a solution uε of (2) which concentrates in a point Qε ∈ ∂Ω andH(Qε) → max∂ΩH , here H denotes the mean curvature of ∂Ω. Moreover in [10], using the LiapunovSchmidt reduction, Li constructs solutions with single peak and multi-peaks on ∂Ω located near ...
متن کاملMultiple Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems
We consider the problem " 2 u ? u + f (u) = 0 in u > 0 in ; @u @ = 0 on @; where is a bounded smooth domain in R N , " > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses boundary spike solutions such that the spike concentrates, as " approaches zero, at a critical point of the mean curvature function H(P); P 2 @. It is also known ...
متن کاملConcentration of solutions for some singularly perturbed Neumann problems
In these notes we describe some methods for studying the asymptotic behavior of solutions to a class of singularly perturbed elliptic problems. We present first the case of concentration at single points, and then at sets of positive dimension.
متن کاملNumerical method for a system of second order singularly perturbed turning point problems
In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. It is assumed that both equations have a turning point at the same point. An appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2019
ISSN: 0036-1410,1095-7154
DOI: 10.1137/18m1219084