Results 51 to 60 of about 724 (89)

The classical overdetermined Serrin problem

, 2017
In this survey we consider the classical overdetermined problem which was studied by Serrin in 1971. The original proof relies on Alexandrov's moving plane method, maximum principles, and a refinement of Hopf's boundary point Lemma.
Nitsch, C., Trombetti, C.
core   +1 more source

Moving planes and sliding methods for fractional elliptic and parabolic equations

Advanced Nonlinear Studies
In this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions.
Chen Wenxiong, Hu Yeyao, Ma Lingwei
doaj   +1 more source

Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficients [PDF]

arXiv, 2011
We prove heat kernel bounds for the operator (1 + |x|^{\alpha})\Delta in R^N, through Nash inequalities and weighted Hardy inequalities.
arxiv  

Maximum principle and one-sign solutions for the elliptic $p$-Laplacian [PDF]

arXiv, 2012
In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.
arxiv  

In Limbo: Three Triangle Centers [PDF]

arXiv, 2014
Yet more candidates are proposed for inclusion in the Encyclopedia of Triangle Centers. Our focus is entirely on simple calculations.
arxiv  

Sliding methods for dual fractional nonlinear divergence type parabolic equations and the Gibbons’ conjecture

Advanced Nonlinear Studies
In this paper, we consider the general dual fractional parabolic problem ∂tαu(x,t)+Lu(x,t)=f(t,u(x,t))inRn×R. ${\partial }_{t}^{\alpha }u\left(x,t\right)+\mathcal{L}u\left(x,t\right)=f\left(t,u\left(x,t\right)\right) \text{in} {\mathbb{R}}^{n}{\times ...
Guo Yahong, Ma Lingwei, Zhang Zhenqiu
doaj   +1 more source

On the Sobolev and Hardy constants for the fractional Navier Laplacian [PDF]

arXiv, 2014
We prove the coincidence of the Sobolev and Hardy constants relative to the "Dirichlet" and "Navier" fractional Laplacians of any real order $m\in(0,\frac{n}{2})$ over bounded domains in $\mathbb R^n$.
arxiv  

Instability of equatorial water waves with an underlying current [PDF]

, 2014
In this paper we use the short-wavelength instability approach to derive an instability threshold for exact trapped equatorial waves propagating eastwards in the presence of an underlying current.
arxiv   +1 more source

Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions

Advances in Nonlinear Analysis
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain can be extended, under suitable conditions, to the case in which the forcing term is sign ...
Díaz Jesús Ildefonso, Hernández Jesús   +1 more
doaj   +1 more source

On a gradient maximum principle for some quasilinear parabolic equations on convex domains [PDF]

arXiv, 2016
We establish a spatial gradient maximum principle for classical solutions to the initial and Neumann boundary value problem of some quasilinear parabolic equations on smooth convex domains.
arxiv