Results 31 to 40 of about 1,686 (103)
Spectral gap of segments of periodic waveguides
, 2006 We consider a periodic strip in the plane and the associated quantum waveguide with Dirichlet boundary conditions. We analyse finite segments of the waveguide consisting of $L$ periodicity cells, equipped with periodic boundary conditions at the ``new ...
D. Borisov +6 more
core +2 more sources
On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets [PDF]
, 2019 Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$.
Berg, M. van den +3 more
core +2 more sources
Symmetry and concentration behavior of ground state in axially symmetric domains
Abstract and Applied Analysis, Volume 2004, Issue 12, Page 1019-1030, 2004., 2004 We let Ω(r) be the axially symmetric bounded domains which satisfy some suitable conditions, then the ground‐state solutions of the semilinear elliptic equation in Ω(r) are nonaxially symmetric and concentrative on one side. Furthermore, we prove the necessary and sufficient condition for the symmetry of ground‐state solutions.
Tsung-Fang Wu
wiley +1 more source
Moderately close Neumann inclusions for the Poisson equation [PDF]
, 2018 open2siWe investigate the behavior of the solution of a mixed problem for the Poisson equation in a domain with two moderately close holes. If ϱ1 and ϱ2 are two positive parameters, we define a perforated domain Ω(ϱ1,ϱ2) by making two small perforations ...
core +1 more source
Coefficients of singularities of the biharmonic problem of Neumann type: case of the crack
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 5, Page 305-313, 2003., 2003 This paper concerns the biharmonic problem of Neumann type in a sector V. We give a representation of the solution u of the problem in a form of a series u = ∑α∈ECα rα ϕα, and the functions ϕα are solutions of an auxiliary problem obtained by the separation of variables.
Wided Chikouche, Aissa Aibèche
wiley +1 more source
Advanced Nonlinear Studies, 2023 We consider the asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity and fulfill previous results under faster convergence rate by Bao et al. [Monge-Ampère equation on exterior domains, Calc. Var PDE.
Liu Zixiao, Bao Jiguang
doaj +1 more source
Spatial boundary problem with the Dirichlet-Neumann condition for a singular elliptic equation
, 2012 The present work devoted to the finding explicit solution of a boundary problem with the Dirichlet-Neumann condition for elliptic equation with singular coefficients in a quarter of ball. For this aim the method of Green's function have been used. Since,
Agostinelli +26 more
core +1 more source
Flat solutions of the 1-Laplacian equation [PDF]
, 2017 For every $f \in L^N(\Omega)$ defined in an open bounded subset $\Omega$ of $\mathbb{R}^N$, we prove that a solution $u \in W_0^{1, 1}(\Omega)$ of the $1$-Laplacian equation ${-}\mathrm{div}{(\frac{\nabla u}{|\nabla u|})} = f$ in $\Omega$ satisfies ...
Orsina, Luigi, Ponce, Augusto C.
core +3 more sources
Unilateral boundary value problems with jump discontinuities
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 30, Page 1933-1941, 2003., 2003 Using the critical point theory of Szulkin (1986), we study elliptic problems with unilateral boundary conditions and discontinuous nonlinearities. We do not use the method of upper and lower solutions. We prove two existence theorems: one when the right‐hand side is nondecreasing and the other when it is nonincreasing.
Nikolaos Halidias
wiley +1 more source
, 2017 In this paper we propose a counterexample to the validity of the Comparison Principle and of the Sub and Supersolution Method for nonlocal problems like the stationary Kirchhoff Equation.
Iturriaga, Leonelo, Massa, Eugenio
core +1 more source