A link between global solvability and solvability over compacts for systems like :
A Note on the kernel of the ...-Neumann operator on strongly pseudoconvex domains.
A Partial Solution of the Pompeiu Problem.
A problem of transversal anisotropic ellipticity
A pseudoconvex domain with bounded solutions for ..., but not admitting ...-estimates.
A remark about elliptic overdeterminated systems
A remark on certain overdetermined systems of partial differential equations
A splitting theory for the space of distributions
The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'
A symmetry result for a fourth order overdetermined boundary value problem.
About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with C1,1 boundary. It is an extension of an earlier result of [Phung, ESAIM: COCV9 (2003) 621–635] for domains of class C∞. Our estimate is established by using a Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Furthermore, we prove that this stability estimate is nearly optimal and induces...
An Approximation Theorem for Integrable Harmonic Vector Fields.
An elementary theory of hyperfunctions and microfunctions
An example of the Heisenberg group
An inverse Neumann problem.
An overdetermined elliptic problem in a domain with countably rectifiable boundary
We examine an elliptic equation in a domain Ω whose boundary ∂Ω is countably (m-1)-rectifiable. We also assume that ∂Ω satisfies a geometrical condition. We are interested in an overdetermined boundary value problem (examined by Serrin [Arch. Ration. Mech. Anal. 43 (1971)] for classical solutions on domains with smooth boundary). We show that existence of a solution of this problem implies that Ω is an m-dimensional Euclidean ball.
Analytic Cycles and Vector Bundles on Non-Compact Algebraic Varieties.
Approximation by Holomorphic Functions on Pseudokonvex Domains with Isolated Degeneracies.
Boundary regularity and compactness for overdetermined problems
Let be either the unit ball or the half ball let be a strictly positive and continuous function, and let and solve the following overdetermined problem:where denotes the characteristic function of denotes the set and the equation is satisfied in the...
Boundary regularity of solutions of the inhomogeneous Cauchy-Riemann equations
Boundary values of holomorphic functions and Cauchy problem for operator in the polydisc