Results 41 to 50 of about 385 (50)

Norm Estimates for Solutions of Elliptic BVPs of the Dirac Operator [PDF]

arXiv, 2014
We present norm estimates for solutions of first and second order elliptic BVPs of the Dirac operator considered over a bounded and smooth domain of the n-dimension Euclidean space. The solutions whose norms to be estimated are in some Sobolev spaces and the boundary conditions as traces of solutions and their derivatives are in some Slobodeckji spaces.
arxiv  

Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system $Δu = W_u(u)$ [PDF]

arXiv, 2014
We study symmetric vector minimizers of the Allen-Cahn energy and establish various results concerning their structure and their asymptotic behavior.
arxiv  

A sign-changing solution for the Schrödinger-Poisson equation [PDF]

arXiv, 2014
We find a sign-changing solution for a class of Schr\"odinger-Poisson system in $\mathbb{R}^3$ as an existence result by minimization in a closed subset containing all the sign-changing solutions of the equation. The proof is based on variational methods in association with the deformation lemma and Miranda's theorem.
arxiv  

Prescribing singularities of weak solutions of a nonlinear elliptic system in the plane [PDF]

arXiv
Inspired by Frehse's [1] 1973 work, we show that his elliptic system $\Delta u = F(u, \nabla u)$ in the plane has bounded weak solutions $u$ with arbitrarily prescribed singular sets.
arxiv  

High energy sign-changing solutions to Schrödinger-Poisson type systems [PDF]

arXiv, 2015
We prove the existence of infinitely many high energy sign-changing solutions for some classes of Schrodinger-Poisson systems in bounded domains, with nonlinearities having subcritical or critical growth. Our approach is variational and relies on an application of a new sign-changing version of the symmetric mountain pass theorem.
arxiv  

Schauder-type estimates for fully nonlinear degenerate elliptic equations [PDF]

arXiv
In this paper, we examine regularity estimates for solutions to fully nonlinear, degenerated elliptic equations, at interior vanishing source points. At these points, we obtain Schauder-type regularity estimates, which depend on the H\"older-like source-ellipticity vanishing rate.
arxiv  

Partial analyticity and nodal sets for nonlinear elliptic systems [PDF]

arXiv, 2015
We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions to the 2-d Euler equation, and analyticity of water waves with and without surface tension.
arxiv  

On a fully nonlinear k-Hessian system of Lane-Emden type [PDF]

arXiv
In this manuscript we prove the existence of solutions to a fully nonlinear system of (degenerate) elliptic equations of Lane-Emden type and discuss a inhomogeneous generalization.
arxiv  

The Friedrichs extension for elliptic wedge operators of second order [PDF]

arXiv, 2015
The paper provides an explicit description of the structure of the domain of the Friedrichs extension of a second order semibounded elliptic wedge operator, initially defined on smooth functions or sections with compact support away from the boundary, under some mild assumptions on the indicial and normal families.
arxiv  

Gradient estimates for solutions of the Lamé system with partially infinite coefficients in dimensions greater than two [PDF]

arXiv, 2016
We establish upper bounds on the blow-up rate of the gradients of solutions of the Lam\'{e} system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero.
arxiv