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.
Poisson kernel characterization of Reifenberg flat chord arc domains
On the hull of holomorphy of an -manifold in
On the elliptic equation
Hardy spaces and the Dirichlet problem on Lipschitz domains.
Our concern in this paper is to describe a class of Hardy spaces H(D) for 1 ≤ p < 2 on a Lipschitz domain D ⊂ R when n ≥ 3, and a certain smooth counterpart of H(D) on R, by providing an atomic decomposition and a description of their duals.
The Dirichlet problem for elliptic equations with drift terms.
We establish absolute continuity of the elliptic measure associated to certain second order elliptic equations in either divergence or nondivergence form, with drift terms, under minimal smoothness assumptions on the coefficients.
Page 1 Next