TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Normally solvable nonlinear boundary value problems
N2  - We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)11 
KW  - Nonlinear Laplace operator
KW  - boundary value problem
KW  - Dirichlet to Neumann operator
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-65077
SN  - 2193-6943
ER  -