Results 1 to 10 of about 9,080 (137)
The Unique Continuation Property of Sublinear Equations [PDF]
SIAM Journal on Mathematical Analysis, 2018 We derive the unique continuation property of a class of semi-linear elliptic equations with non-Lipschitz nonlinearities. The simplest type of equations to which our results apply is given as $-Δu = |u|^{σ-1} u$ in a domain $Ω\subset \mathbb{R}^N$, with $0 \le σ<1$.
Tobias Weth, Nicola Soave
exaly +3 more sources
On the unique continuation property for a nonlinear dispersive system
Electronic Journal of Qualitative Theory of Differential Equations, 2005 We solve the following problem: If $(u,\,v)=(u(x,\,t),\,v(x,\,t))$ is a solution of the Dispersive Coupled System with $t_{1}
A. Kozakevicius +1 more
doaj +3 more sources
Strong unique continuation property for stochastic parabolic equations
Science China MathematicsWe establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation property of stochastic partial differential equations.
Qi Lu
exaly +3 more sources
Unique continuation property for the elasticity with general residual stress
Inverse Problems and Imaging, 2009 We prove the unique continuation property for the isotropic elasticity system with arbitrarily large residual stress. This work improves the result obtained in [10] where the residual stress is assumed to be small.
Jenn-Nan Wang, GÜNTHER Uhlmann
exaly +3 more sources
On Some Fractional Magnetic Problems
Pan-American Journal of Mathematics, 2023 In this article, we study existence of weak solutions and the unique continuation property of the nonlocal fractional magnetic equation. First, we use a variational technique to prove existence of weak solutions for the fractional Schrödinger equation ...
Frédéric D. Y. Zongo +2 more
doaj +1 more source
Weak damping for the Korteweg-de Vries equation
Electronic Journal of Qualitative Theory of Differential Equations, 2021 For more than 20 years, the Korteweg–de Vries equation has been intensively explored from the mathematical point of view. Regarding control theory, when adding an internal force term in this equation, it is well known that the Korteweg–de Vries equation ...
Roberto de A. Capistrano Filho
doaj +1 more source
Unique continuation property for biharmonic hypersurfaces in spheres
Annals of Global Analysis and Geometry, 2021 We study properties of non-minimal biharmonic hypersurfaces of spheres. The main result is a CMC Unique Continuation Theorem for biharmonic hypersurfaces of spheres. We then deduce new rigidity theorems to support the Conjecture that biharmonic submanifolds of Euclidean spheres must be of constant mean curvature.
Hiba Bibi, Eric Loubeau, Cezar Oniciuc
openaire +3 more sources
Higher-order fractional Laplacians: An overview
Bruno Pini Mathematical Analysis Seminar, 2022 We summarize some of the most recent results regarding the theory of higher-order fractional Laplacians, i.e., the operators obtained by considering (non-integer) powers greater than 1 of the Laplace operator.
Nicola Abatangelo
doaj +1 more source
The unique continuation property for a nonlinear equation on trees [PDF]
Journal of the London Mathematical Society, 2014 In this paper we study the game $p-$Laplacian on a tree, that is, $$ u(x)=\fracα2\left\{\max_{y\in §(x)}u(y) + \min_{y\in §(x)}u(y)\right\} + \fracβ{m}\sum_{y\in §(x)} u(y), $$ here $x$ is a vertex of the tree and $S(x)$ is the set of successors of $x$. We study the family of the subsets of the tree that enjoy the unique continuation property, that is,
Leandro M. Del Pezzo +2 more
openaire +4 more sources
Multiscale Unique Continuation Properties of Eigenfunctions [PDF]
, 2015 Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schrödinger operators and control theory. We review recent results and announce new ones regarding quantitative unique continuation principles for partial differential equations with an underlying multiscale structure.
Borisov, Denis +4 more
openaire +3 more sources