Symmetry and Overdetermined Boundary Value Problems.
The Edge-of-Wedge Theorem for Systems of Constant Coefficient Partial Differential Operators. II.
The Edge-of-Wedge Theorem for Systems of Constant Coefficient Partial Differential Operators. I.
The overdetermined Cauchy problem
We consider the (characteristic and non-characteristic) Cauchy problem for a system of constant coefficients partial differential equations with initial data on an affine subspace of arbitrary codimension. We show that evolution is equivalent to the validity of a principle on the complex characteristic variety and we study the relationship of this condition with the one introduced by Hörmander in the case of scalar operators and initial data on a hypersurface.
Two symmetry problems in potential theory.
Universal prolongation of linear partial differential equations on filtered manifolds
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.
Интегральные представления для операторов с конечномерным ядром.
Энергетический метод для трехмерных эллиптических уравнений с несимметричными тензорными коэффинциентами.