1,363 research outputs found
Optimal boundary holes for the Sobolev trace constant
In this paper we study the problem of minimizing the Sobolev trace Rayleigh
quotient among
functions that vanish in a set contained on the boundary 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.Comment: 22 page
An optimization problem with volume constrain in Orlicz spaces
We consider the optimization problem of minimizing in the class of functions , with a constrain on the
volume of . The conditions on the function allow for a different
behavior at
0 and at . We consider a penalization problem, and we prove that for
small values of the penalization parameter, the constrained volume is attained.
In this way we prove that every solution is locally Lipschitz continuous
and that the free boundary, , is smooth
Estimates for the Sobolev trace constant with critical exponent and applications
In this paper we find estimates for the optimal constant in the critical
Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow
\|u\|^p_{W^{1,p}(\Omega)} that are independent of . This estimates
generalized those of [3] for general . Here is the
critical exponent for the immersion and is the space dimension. Then we
apply our results first to prove existence of positive solutions to a nonlinear
elliptic problem with a nonlinear boundary condition with critical growth on
the boundary, generalizing the results of [16]. Finally, we study an optimal
design problem with critical exponent.Comment: 22 pages, submitte
A constrained shape optimization problem in Orlicz-Sobolev spaces
In this manuscript we study the following optimization problem: given a bounded and regular domain Ω⊂RN we look for an optimal shape for the “W−vanishing window” on the boundary with prescribed measure over all admissible profiles in the framework of the Orlicz-Sobolev spaces associated to constant for the “Sobolev trace embedding”. In this direction, we establish existence of minimizer profiles and optimal sets, as well as we obtain further properties for such extremals. Finally, we also place special emphasis on analyzing the corresponding optimization problem involving an “A−vanishing hole” (inside the domain) with volume constraint.Fil: Da Silva, Joao Vitor. Universidade do Brasília; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Salort, Ariel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Spedaletti, Juan Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentin
A variational method for second order shape derivatives
We consider shape functionals obtained as minima on Sobolev spaces of
classical integrals having smooth and convex densities, under mixed
Dirichlet-Neumann boundary conditions. We propose a new approach for the
computation of the second order shape derivative of such functionals, yielding
a general existence and representation theorem. In particular, we consider the
p-torsional rigidity functional for p grater than or equal to 2.Comment: Submitted paper. 29 page
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