Results 61 to 70 of about 159 (128)

Boundary charges and integral identities for solitons in (d+1)-dimensional field theories

Nuclear Physics B, 2017
We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions.
Sven Bjarke Gudnason, Zhifeng Gao, Yisong Yang   +2 more
doaj   +1 more source

Boundary Regularity, Pohozaev Identities and Nonexistence Results

, 2017
In this expository paper we survey some recent results on Dirichlet problems of the form $Lu=f(x,u)$ in $Ω$, $u\equiv0$ in $\mathbb R^n\backslashΩ$. We first discuss in detail the boundary regularity of solutions, stating the main known results of Grubb and of the author and Serra. We also give a simplified proof of one of such results, focusing on the
openaire   +2 more sources

Integrability of Einstein deformations and desingularizations

Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 177-220, January 2024.
Abstract We study the question of the integrability of Einstein deformations and relate it to the question of the desingularization of Einstein metrics. Our main application is a negative answer to the long‐standing question of whether or not every Einstein 4‐orbifold (which is an Einstein metric space in a synthetic sense) is limit of smooth Einstein ...
Tristan Ozuch
wiley   +1 more source

Existence of a ground-state solution for a quasilinear Schrödinger system

Frontiers in Physics
In this paper, we consider the following quasilinear Schrödinger system.−Δu+u+k2Δ|u|2u=2αα+β|u|α−2u|v|β,x∈RN,−Δv+v+k2Δ|v|2v=2βα+β|u|α|v|β−2v,x∈RN,where k < 0 is a real constant, α > 1, β > 1, and α + β < 2*.
Xue Zhang, Jing Zhang, Jing Zhang, Jing Zhang   +3 more
doaj   +1 more source

Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations

Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 3-36, January 2024.
Abstract We consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is well‐known that: ‐For n=2$n=2$, there exist Morse index 1 solutions whose L∞$L^\infty$ norm goes to infinity. ‐For n≥3$n \ge 3$, uniform boundedness holds in the subcritical case for power‐type nonlinearities, while for ...
Alessio Figalli, Yi Ru‐Ya Zhang
wiley   +1 more source

Uniqueness for a semilinear elliptic equation in non-contractive domains under supercritical growth conditions

Electronic Journal of Differential Equations, 1999
We apply the Pohozaev identity to sub-domains of a tubular neighbourhood of a closed or broken curve in $Bbb R^n$ and establish uniqueness results for the smooth solutions of the Dirichlet problem for $-Delta u+|u|^{p-1}u=0$.
Kewei Zhang
doaj  

Nondegeneracy of the solutions for elliptic problem with critical exponent

Boundary Value Problems
This paper deals with the following nonlinear elliptic equation: − Δ u = Q ( | y ′ | , y ″ ) u N + 2 N − 2 , u > 0 , in R N , u ∈ D 1 , 2 ( R N ) , $$ -\Delta u=Q(|y'|,y'')u^{\frac{N+2}{N-2}},\,\,u>0,\,\,\text{in}\,{ \mathbb{R}}^{N},\,\,u\in D^{1,2 ...
Qingfang Wang
doaj   +1 more source

Overdetermined boundary value problems with strongly nonlinear elliptic PDE

Electronic Journal of Qualitative Theory of Differential Equations, 2012
We consider the strongly nonlinear elliptic Dirichlet problem in a connected bounded domain, overdetermined with the constant Neumann condition $F(\nabla u)=c$ on the boundary. Here $F$ is convex and positively homogeneous of degree 1, and its polar $F^
Boqiang Lv, Fengquan Li, Weilin Zou
doaj   +1 more source

Existence of regular and singular bound state solutions to a quasilinear equation

Boundary Value Problems
The existence of regular and singular bound state solutions to △ p u + f ( u ) = 0 , r ∈ R n ∖ { 0 } $$ \triangle _{p}u+f(u)=0,~~~r\in \mathbb{R}^{n}\backslash \{0\} $$ is considered. Our result concerns the solution according to its behavior as r → 0 $r\
Wei-Chuan Wang
doaj   +1 more source

The Pohozaev identity for mixed local-nonlocal operators

Journal of Mathematical Analysis and Applications
15 ...
openaire   +2 more sources