Lie symmetries of a third order PDE system
Reza Dastranj
In this paper we show that a third order PDE system that is a general form of a CR-geometry PDE system has at most a ten-dimensional Lie symmetry algebra. We also show that this estimate is precise.
Lp estimates for the Caffarelli-Silvestre extension operators
Giorgio Metafune, Luigi Negro, Chiara Spina
We study elliptic and parabolic problems governed by the singular elliptic operators Delta_x+c\yD_y-b\y^2 on the half-space R^{N+1}_+.
Regular Global Solutions for A Generalized KdV Equation Posed on A Half-Line
Nikolai Larkin
An initial-boundary value problem for a generalized KdV equation posed on a half-line is considered. Existence and uniqueness of global regular solutions for arbitrary smooth initial data are established.
Multiple solutions for a class of semilinear elliptic equations
Yifu Wang
By using truncation technique, minimization method and Morse theory, we obtain three nontrivial solutions for a class of semilinear elliptic equations.
Uniqueness in determining the orders of time and spatial fractional derivatives
Masahiro Yamamoto
We prove the uniqueness in determining both orders of fractional time derivatives and spatial derivatives in diffusion equations by pointwise data. The proof relies on the eigenfunction expansion and the asymptotics of the Mittag-Leffler function.
Remark on the exponential decay of the solutions of the damped wave equation
Giovanni Cimatti
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also presented.
Serrin's type problems in warped product manifolds
Alberto Farina, Alberto Roncoroni
In this paper we consider Serrin's overdetermined problems in warped product manifolds and we prove Serrin's type rigidity results by using the P-function approach introduced by Weinberger.
A note on the convergence of almost minimal sets
Yangqin Fang
In this paper, we will show that Hausdorff convergence and varifold convergence coincide on the class of almost minimal sets.
Bifurcation of rotating patches from Kirchhoff vortices
Taoufik Hmidi, Joan Mateu
In this paper we prove the existence of countable branches of rotating patches bifurcating from the ellipses at some implicit angular velocities.
A remark on unique continuation for the Cauchy-Riemann operator
Ihyeok Seo
In this note we obtain a unique continuation result for the differential inequality $|\bar{\partial}u|\leq|Vu|$, where $\bar{\partial}=(i\partial_y+\partial_x)/2$ denotes the Cauchy-Riemann operator and $V(x,y)$ is a function in $L^2(\mathbb{R}^2)$.
Equilibria and Their Stability for a Viscous Droplet Model
Patrick Guidotti
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction argument.
On solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives
Andrej A. Kon'kov
We obtain estimates and blow-up conditions for solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives
About Brezis-Merle Problem with Lipschitz condition
Samy Skander Bahoura
We give blow-up analysis for a Brezis-Merle's problem on the boundary. Also we give a proof of a compactness result with Lipschitz condition and weaker assumption on the regularity of the domain (smooth domain or $ C^{2,α} $ domain).
On the global well-posedness of the critical quasi-geostrophic equation
Hamadi Abidi, Taoufik Hmidi
We prove the global well-posedness of the critical dissipative quasi-geostrophic equation for large initial data belonging to the critical Besov space $\dot B^0_{\infty,1}(\RR^2).$
Multiplicity of solutions of a zero mass nonlinear equation on a Riemannian manifold
Daniela Visetti
The relation between the number of solutions of a nonlinear equation on a Riemannian manifold and the topology of the manifold itself is studied. The technique is based on Ljusternik-Schnirelmann category and Morse theory.
Weighted L^p decay estimates of solutions to the wave equation with a potential
Fernando Cardoso, Georgi Vodev
We obtain large time decay estimates on weighted $L^p$ spaces for solutions to the wave equation with real-valued potential $V(x)=O(|x|^{-2-a})$, $a>0$, for $|x|>1$.
Effet d'une perturbation non lineaire sur l'obtention d'une Estimation Uniforme
Samy Skander Bahoura
To have an uniform estimate for the solutions of the scalar curvature equation perturbed by a non linear term, we give some minimal condition on the scalar curvature.
Remark on the Kato smoothing effect for Schrödinger equation with superquadratic potentials
Luc Robbiano, Claude Zuily
The aim of this note is to extend recent results of Yajima-Zhang \cite{Y-Z1, Y-Z2} on the 1/2- smoothing effect for Schrödinger equation with potential growing at infinity faster than quadratically.
Complex-valued solutions of the Benjamin-Ono equation
Alexandru D. Ionescu Carlos E. Kenig
We prove that the Benjamin-Ono initial-value problem is locally well-posed for small, complex-valued data in Sobolev spaces with special low-frequency structure.
Boundedness of the Hessian of a biharmonic function in a convex domain
Svitlana Mayboroda, Vladimir Maz'ya
We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.