The Calderón Projector for an Elliptic Operator in Divergence Form.
The Calderón-Zygmund theorem and parabolic equations in -spaces
A Banach-space version of the Calderón-Zygmund theorem is presented and applied to obtaining apriori estimates for solutions of second-order parabolic equations in -spaces.
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.
The Dirichlet problem in the dispersion of gas exhalations over a wet hilly surface
The domain of the Ornstein-Uhlenbeck operator on an -space with invariant measure
We show that the domain of the Ornstein-Uhlenbeck operator on
The first eigenvalue of -Laplacian systems with nonlinear boundary conditions.
The Generalized Ahlfors-Heins Theorem in Certain d-Dimensional Cones.
The Green Function for Uniformly Elliptic Equations.
The index of isolated critical points and solutions of elliptic equations in the plane
The Scattering of Classical Waves from Inhomogeneous media.
The solution of Kato's conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian)
Kato’s conjecture, stating that the domain of the square root of any accretive operator with bounded measurable coefficients in is the Sobolev space , i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, McIntosh and the author. These notes present the result and explain the strategy of proof.
The spectral distribution of a globally elliptic operator
Theoretical foundation of the weighted Laplace inpainting problem
Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed, where the differential operator consists of a point-wise convex combination of the Laplacian and the known image data. We provide the first detailed analysis on existence and uniqueness of solutions for the arising mixed boundary value problem. Our approach considers...
To the inversion of Gårding theorem
Towards the Cauchy problem for the Laplace equation
Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems
This text is a survey of recent results on traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity. We present the existence, nonexistence and stability results and we describe the main ideas used in proofs.