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pro vyhledávání: '"Jerrard, Robert"'
Alexandrov's estimate states that if $\Omega$ is a bounded open convex domain in ${\mathbb R}^n$ and $u:\bar \Omega\to {\mathbb R}$ is a convex solution of the Monge-Ampere equation $\det D^2 u = f$ that vanishes on $\partial \Omega$, then \[ |u(x) -
Externí odkaz:
http://arxiv.org/abs/2310.20612
It is well-known that under suitable hypotheses, for a sequence of solutions of the (simplified) Ginzburg-Landau equations $-\Delta u_\varepsilon +\varepsilon^{-2}(|u_\varepsilon|^2-1)u_\varepsilon = 0$, the energy and vorticity concentrate as $\vare
Externí odkaz:
http://arxiv.org/abs/2101.03575
Autor:
Contreras, Andres, Jerrard, Robert L.
A central focus of Ginzburg-Landau theory is the understanding and characterization of vortex configurations. On a bounded domain $\Omega\subseteq \mathbb{R}^2,$ global minimizers, and critical states in general, of the corresponding energy functiona
Externí odkaz:
http://arxiv.org/abs/1911.06914
Autor:
Ignat, Radu, Jerrard, Robert L.
We study a variational Ginzburg-Landau type model depending on a small parameter $\varepsilon>0$ for (tangent) vector fields on a $2$-dimensional Riemannian manifold $S$. As $\varepsilon\to 0$, these vector fields tend to have unit length so they gen
Externí odkaz:
http://arxiv.org/abs/1910.02921
Autor:
Jerrard, Robert L., Maor, Cy
Publikováno v:
Ann Glob Anal Geom (2019) 56 : 351--360
We study the geodesic distance induced by right-invariant metrics on the group $\operatorname{Diff}_c(M)$ of compactly supported diffeomorphisms of a manifold $M$, and show that it vanishes for the critical Sobolev norms $W^{s,n/s}$, where $n$ is the
Externí odkaz:
http://arxiv.org/abs/1901.04121
We consider the wave equation $\varepsilon^2(-\partial_t^2 + \Delta)u + f(u) = 0$ for $0<\varepsilon\ll 1$, where $f$ is the derivative of a balanced, double-well potential, the model case being $f(u) = u-u^3$. For equations of this form, we construc
Externí odkaz:
http://arxiv.org/abs/1808.02471
Autor:
Jerrard, Robert L., Maor, Cy
Publikováno v:
Ann Glob Anal Geom (2019) 55: 631--656
We study the geodesic distance induced by right-invariant metrics on the group $\operatorname{Diff}_\text{c}(M)$ of compactly supported diffeomorphisms, for various Sobolev norms $W^{s,p}$. Our main result is that the geodesic distance vanishes ident
Externí odkaz:
http://arxiv.org/abs/1805.01410
Publikováno v:
Nonlinear Differ. Equ. Appl. (2018) 25: 15
We improve on recent results that establish the existence of solutions of certain semilinear wave equations possessing an interface that roughly sweeps out a timelike surface of vanishing mean curvature in Minkowski space. Compared to earlier work, w
Externí odkaz:
http://arxiv.org/abs/1708.06804
Autor:
Ignat, Radu, Jerrard, Robert L.
We study a variational Ginzburg-Landau type model depending on a small parameter $\epsilon>0$ for (tangent) vector fields on a $2$-dimensional Riemannian surface. As $\epsilon\to 0$, the vector fields tend to be of unit length and will have singular
Externí odkaz:
http://arxiv.org/abs/1701.06546