INVESTIGADORES
FERNANDEZ BONDER Julian
artículos
Título:
Optimal boundary holes for the Sobolev trace constant.
Autor/es:
LEANDRO DEL PEZZO; JULIAN FERNANDEZ BONDER; WLADIMIR NEVES
Revista:
JOURNAL OF DIFFERENTIAL EQUATIONS
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Lugar: Amsterdam; Año: 2011 p. 2327 - 2351
ISSN:
0022-0396
Resumen:
In this paper we study the problem of minimizing the Sobolev
trace Rayleigh quotient ||u||_{1,p} / ||u||_{p} among functions that vanish
in a set contained on the boundary of the domain of given boundary measure.
We prove existence of extremals for this problem, and analyze some particular
cases where information about the location of the optimal boundary set
can be given. Moreover, we further study the shape derivative of the Sobolev
trace constant under regular perturbations of the boundary set.