Eugene B. Fabes: 1937-1997.
Existence of Local Smooth Solution for a Generalized Zakharov System.
Maximal operators defined by Fourier multipliers
Weak star and bounded weak star continuity of Banach algebra products
Convex domains and unique continuation at the boundary.
We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.
Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains
The Dirichlet problem for the biharmonic equation in a Lipschitz domain
Flatness of Domains and Doubling Properties of Measures Supported on their Boundary, with Applications to Harmonic Measure.
Local well posedness of nonlinear Schrödinger equations
On the local and global well-posedness theory for the KP-I equation
Boundary value problems for elliptic equations.
In this note I will describe some recent results, obtained jointly with R. Fefferman and J. Pipher [RF-K-P], on the Dirichlet problem for second-order, divergence form elliptic equations, and some work in progress with J. Pipher [K-P] on the corresponding results for the Neumann and regularity problems.
Global Well-posedness, scattering and blow up for the energy-critical, focusing, non-linear Schrödinger and wave equations
Some recent quantitative unique continuation theorems
Local Well-Posedness for Higher Order Nonlinear Dispersive Systems.
The Absolute Continuity of Elliptic Measure Revisited.
The Local Hull of Holomorphy of a Surface in the Space of Two Complex Variables.
The Neumann problem for elliptic equations with non-smooth coefficients.
Hardy spaces, A..., and singular integrals on chord-arc domains
The functional calculus for the laplacian on Lipschitz domains
Ψ-pseudodifferential operators and estimates for maximal oscillatory integrals
We define a class of pseudodifferential operators with symbols a(x,ξ) without any regularity assumptions in the x variable and explore their boundedness properties. The results are applied to obtain estimates for certain maximal operators associated with oscillatory singular integrals.
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