RT Book, Section
T1 Remarks on the Monge-Ampère equation: some free boundary problems in geometry
A1 Díaz Díaz, Gregorio
A1 Díaz Díaz, Jesús Ildefonso
AB This paper deals with several qualitative properties of solutions of some stationary and parabolic equations associated to the Monge-Ampère operator. Mainly, we focus our attention in the occurrence of a free boundary (separating the region where the solution u is locally a hyperplane, and so were the Hessian D2u is vanishing from the rest of the domain). Among other thinfs, we take advantage of these proceedings to give a detailed version of some results already announced long time ago when dealing wiht other fully nonlinear equations (see the 1979 àèr by the authors on other parabolic equations, remark 2.25 of the 1985 monograph by the second author and the 1985 paper by the first author. In particular, our results apply to suitable formulations of the Gauss curvature flow and of the worn stones problems intensively studied in the literature.
PB UCM
SN 978-84-695-4421-1
YR 2012
FD 2012
LK https://hdl.handle.net/20.500.14352/45361
UL https://hdl.handle.net/20.500.14352/45361
LA eng
NO Unión Europea. FP7
NO Ministerio de Ciencia e Innovación (MICINN)
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 3 may 2024