Stability of classes of mappings and Hölder continuity of higher derivatives of elliptic solutions to systems of nonlinear differential equations.
We consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the Navier-Stokes system with a feed-back body forces field which depends on the velocity field. Since the presence of this type of non-linear terms is not standard in the fluid mechanics literature, we start by establishing some results about existence and uniqueness of weak solutions. Then, we prove how this fluid can be stopped at a finite distance of the semi-infinite strip entrance by...
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
In the present paper we seek the bounce trajectories in a convex set which assume assigned positions in two fixed time instants. We find sufficient conditions in order to obtain the existence of infinitely many bounce trajectories.
Let be the boundary of the unit ball of . A set of second order linear partial differential operators, tangential to , is explicitly given in such a way that, for , the corresponding PDE caractherize the trace of the solution of the pluriharmonic problem (either “in the large” or “local”), relative to .