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6 papers · 2 filters
The Dirichlet problem for the Bellman equation at resonance
Scott N. Armstrong
We generalize the Donsker-Varadhan minimax formula for the principal eigenvalue of a uniformly elliptic operator in nondivergence form to the first principal half-eigenvalue of a f…
On the 2d Zakharov system with L^2 Schrödinger data
Ioan Bejenaru, Sebastian Herr, Justin Holmer +1
We prove local in time well-posedness for the Zakharov system in two space dimensions with large initial data in L^2 x H^{-1/2} x H^{-3/2}. This is the space of optimal regularity…
Renormalization and blow up for the critical Yang-Mills problem
Joachim Krieger, Wilhelm Schlag, Daniel Tataru
We consider the Yangs-Mills equations in 4+1 dimensions. This is the energy critical case and we show that it admits a family of solutions which blow up in finite time. They are ob…
Decay estimates for variable coefficient wave equations in exterior domains
Jason Metcalfe, Daniel Tataru
In this article we consider variable coefficient, time dependent wave equations in exterior domains. We prove localized energy estimates if the domain is star-shaped and global in…
Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations
Scott N. Armstrong
We study the fully nonlinear elliptic equation in a smooth bounded domain , under the assumption the nonlinearity is uniformly elliptic and positively h…
Gradient NLW on curved background in 4+1 dimensions
Dan-Andrei Geba, Daniel Tataru
We obtain a sharp local well-posedness result for the Gradient Nonlinear Wave Equation on a nonsmooth curved background. In the process we introduce variable coefficient versions o…