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Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case
We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1 is smaller than that of the standing wave…
A bilinear estimate with applications to the KdV equation
u(x, 0) = u0(x), where u0 ∈ H(R). Our principal aim here is to lower the best index s for which one has local well posedness in H(R), i.e. existence, uniqueness, persistence and continuous dependence…
The local regularity of solutions of degenerate elliptic equations
- E. Fabes, C. Kenig, R. Serapioni
- Mathematics
- 1982
The Inhomogeneous Dirichlet Problem in Lipschitz Domains
- D. Jerison, C. Kenig
- Mathematics
- 15 May 1995
Boundary behavior of harmonic functions in non-tangentially accessible domains
- D. Jerison, C. Kenig
- Mathematics
- 1 October 1982
Well-posedness of the initial value problem for the Korteweg-de Vries equation
(1.1) &ItU + axu + U1xU = O, x, t E R { u(x, 0) = uo(x). The KdV equation, which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves [21], has been…
Oscillatory integrals and regularity of dispersive equations
This paper is concerned with oscillatory integrals and their relationship with the local and global smoothing properties of dispersive equations. Also we shall study some applications of these…
Multilinear estimates and fractional integration
and the pi are additionally restricted by the requirement r > 23 (instead of r > 12 ). The condition r > 2 3 is a consequence of the methods used in their proof, and may not be necessary; these…
Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems
- C. Kenig
- Mathematics
- 7 July 1994
Introduction Divergence form elliptic equations Some classes of examples and their perturbation theory Epilogue: Some further results and open problems References.
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