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11 papers · 2 filters
Harmonic maps in connection of phase transitions with higher dimensional potential wells
Fanghua Lin, Changyou Wang
This is in the sequel of authors' paper \cite{LPW} in which we had set up a program to verify rigorously some formal statements associated with the multiple component phase transit…
Equivalence of the ellipticity conditions for geometric variational problems
Antonio De Rosa, Sławomir Kolasiński
We exploit the so called atomic condition, recently defined by De Philippis, De Rosa, and Ghiraldin in [Comm. Pure Appl. Math.] and proved to be necessary and sufficient for the va…
Vorticity measures and the inviscid limit
Peter Constantin, Milton Lopes Filho, Helena Nussenzveig Lopes +1
We consider a sequence of Leray-Hopf weak solutions of the 2D Navier-Stokes equations on a bounded domain, in the vanishing viscosity limit. We provide sufficient conditions on the…
On the boundary behavior of mass-minimizing integral currents
Camillo De Lellis, Guido De Philippis, Jonas Hirsch +1
Let be a smooth Riemannian manifold, a smooth closed oriented submanifold of codimension higher than and an integral area-minimizing current in which b…
Homogenization, linearization and large-scale regularity for nonlinear elliptic equations
Scott Armstrong, Sam Ferguson, Tuomo Kuusi
We consider nonlinear, uniformly elliptic equations with random, highly oscillating coefficients satisfying a finite range of dependence. We prove that homogenization and lineariza…
On the global behavior of weak null quasilinear wave equations
Yu Deng, Fabio Pusateri
We consider a class of quasilinear wave equations in space-time dimensions that satisfy the "weak null condition" as defined by Lindblad and Rodnianski \cite{LR1}, and study…