Results 1 to 10 of about 325 (25)
Characterization of balls through optimal concavity for potential functions [PDF]
Proc. Amer. Math. Soc. 143 (2015), 2012 Let $p\in(1,n)$. If $\Omega$ is a convex domain in $\rn$ whose $p$-capacitary potential function $u$ is $(1-p)/(n-p)$-concave (i.e. $u^{(1-p)/(n-p)}$ is convex), then $\Omega$ is a ball.
arxiv +1 more source
Symmetry in variational principles and applications [PDF]
, 2011 We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications to PDEs, fixed point theory and geometric analysis.
arxiv +1 more source
Symmetry and uniqueness of nonnegative solutions of some problems in the halfspace [PDF]
Journal of Mathematical Analysis and Applications, 403 (2013),
215--233, 2012 We derive some 1-D symmetry and uniqueness or non-existence results for nonnegative solutions of some elliptic system in the halfspace $\R^N_+$ in low dimension. Our method is based upon a combination of Fourier series and Liouville theorems.
arxiv +1 more source
Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems [PDF]
Journal of Nonlinear Mathematical Physics, Vol. 21, No. 4
(December 2014), 643--671, 2014 We present a complete description of $2$-dimensional equations that arise as symmetry reductions of fourf $3$-dimensional Lax-integrable equations: (1) the universal hierarchy equation~$u_{yy}=u_zu_{xy}-u_yu_{xz}$; (2) the 3D rdDym equation $u_{ty}=u_xu_{xy}-u_yu_{xx}$; (3) The basic Veronese web equation $u_{ty}=u_tu_{xy}-u_yu_{tx}$; (4) Pavlov's ...
arxiv +1 more source
Harmonic approximation and improvement of flatness in a singular perturbation problem [PDF]
arXiv, 2014 We study the De Giorgi type conjecture, that is, one dimensional symmetry problem for entire solutions of an two components elliptic system in $\mathbb{R}^n$, for all $n\geq 2$. We prove that, if a solution $(u,v)$ has a linear growth at infinity, then it is one dimensional, that is, depending only on one variable. The main ingredient is an improvement
arxiv
A new proof of Savin's theorem on Allen-Cahn equations [PDF]
arXiv, 2014 In this paper we establish an improvement of tilt-excess decay estimate for the Allen-Cahn equation, and use this to give a new proof of Savin's theorem on the uniform $C^{1,\alpha}$ regularity of flat level sets, which then implies the one dimensional symmetry of minimizers in $\mathbb{R}^n$ for $n\leq 7$.
arxiv
On the symmetry of minimizers in constrained quasi-linear problems [PDF]
arXiv, 2010 We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems.
arxiv
On Ekeland's variational principle [PDF]
arXiv, 2010 For proper lower semi-continuous functionals bounded below which do not increase upon polarization, an improved version of Ekeland's variational principle can be formulated in Banach spaces, which provides almost symmetric points.
arxiv
Multiple $\mathbb{S}^{1}$-orbits for the Schrödinger-Newton system [PDF]
arXiv, 2013 We prove existence and multiplicity of symmetric solutions for the \emph{Schr\"odinger-Newton system} in three dimensional space using equivariant Morse theory.
arxiv
Symmetry breaking of solutions of non-cooperative elliptic systems [PDF]
arXiv, 2013 In this article we study the symmetry breaking phenomenon of solutions of noncooperative elliptic systems. We apply the degree for G-invariant strongly indefinite functionals to obtain simultaneously a symmetry breaking and a global bifurcation phenomenon.
arxiv