• search hit 71 of 960
Back to Result List

A variational approach to the Cauchy problem for nonlinear elliptic differential equations

  • We discuss the relaxation of a class of nonlinear elliptic Cauchy problems with data on a piece S of the boundary surface by means of a variational approach known in the optimal control literature as "equation error method". By the Cauchy problem is meant any boundary value problem for an unknown function y in a domain X with the property that the data on S, if combined with the differential equations in X, allow one to determine all derivatives of y on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We also admit overdetermined elliptic systems, in which case the set of those Cauchy data on S for which the Cauchy problem is solvable is very "thin". For this reason we discuss a variational setting of the Cauchy problem which always possesses a generalised solution.

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics
Author:Ibrahim Ly, Nikolai Nikolaevich TarkhanovORCiDGND
Document Type:Article
Year of first Publication:2009
Year of Completion:2009
Release Date:2017/03/25
Source:Journal of inverse and ill-posed problems. - ISSN 0928-0219. - 17 (2009), 6, S. 595 - 610
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Informatik und Computational Science
Peer Review:Referiert
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Informatik