We study the regularity up to the boundary of solutions to the nonlinear boundary value problem consisting in finding a harmonic function u in a domain with given gradient's modulus g on the boundary of the domain. This problem finds its application in the study of geophysical and geomagnetic surveys. If g is Hölder continuous and strictly positive, we prove that u is in the class of differentiable functions with Hölder continuous derivatives in the closure of the domain. Anexample shows that this is no longer true if g has some zeroes on the boundary. In this case u is proved to be of class C1 .
A fully nonlinear boundary value problem for the Laplace equation in dimension two / R. MAGNANINI. - In: APPLICABLE ANALYSIS. - ISSN 0003-6811. - STAMPA. - 39:(1990), pp. 185-192.
A fully nonlinear boundary value problem for the Laplace equation in dimension two
MAGNANINI, ROLANDO
1990
Abstract
We study the regularity up to the boundary of solutions to the nonlinear boundary value problem consisting in finding a harmonic function u in a domain with given gradient's modulus g on the boundary of the domain. This problem finds its application in the study of geophysical and geomagnetic surveys. If g is Hölder continuous and strictly positive, we prove that u is in the class of differentiable functions with Hölder continuous derivatives in the closure of the domain. Anexample shows that this is no longer true if g has some zeroes on the boundary. In this case u is proved to be of class C1 .I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.