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12 papers · 2 filters
Partial Regularity for Harmonic Maps into Spheres at a Singular or Degenerate Free Boundary
Roger Moser, James Roberts
We prove partial regularity of weakly stationary harmonic maps with (partially) free boundary data on manifolds where the domain metric may degenerate or become singular along the…
Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions
Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva
Using a generalisation of the classical notion of Dirichlet-to-Neumann map and the related formulae for the resolvents of boundary-value problems, we analyse the asymptotic behavio…
Some non-homogeneous Gagliardo-Nirenberg inequalities and application to a biharmonic non-linear Schrödinger equation
Antonio J. Fernández, Louis Jeanjean, Rainer Mandel +1
We study the standing waves for a fourth-order Schrödinger equation with mixed dispersion that minimize the associated energy when the norm (the \textit{mass}) } is kept fixe…
Global bifurcation of solitary waves for the Whitham equation
Tien Truong, Erik Wahlén, Miles H. Wheeler
The Whitham equation is a nonlocal shallow water-wave model which combines the quadratic nonlinearity of the KdV equation with the linear dispersion of the full water wave problem.…
Travelling and rotating solutions to the generalized inviscid surface quasi-geostrophic equation
Weiwei Ao, Juan Davila, Manuel del Pino +2
For the generalized surface quasi-geostrophic equation $$\left\{ \begin{aligned} & \partial_t θ+u\cdot \nabla θ=0, \quad \text{in } \mathbb{R}^2 \times (0,T), \\ & u=\nabla^\perp ψ…
Global bifurcation of anti-plane shear fronts
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
We consider anti-plane shear deformations of an incompressible elastic solid whose reference configuration is an infinite cylinder with a cross section that is unbounded in one dir…