Wolfgang Tutschke

Interior Estimates in The Theory of Partial Differential Equations and Their Application to Initial Value Problems

abstract:
The present paper is aimed at solving initial value problems by the contraction-mapping principle in case an interior estimate is true in the function space under consideration.

Mathematics Subject Classification: 35A10, 35F10, 30G20, 35J30.

Key words and phrases: Initial value problems of Cauchy--Kovalevskaya type, conical evolution, interior estimates of solutions of elliptic equations.