90 research outputs found
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
Characterization of stadium-like domains via boundary value problems for the infinity Laplacian
We give a complete characterization, as "stadium-like domains", of convex
subsets of where a solution exists to Serrin-type
overdetermined boundary value problems in which the operator is either the
infinity Laplacian or its normalized version. In case of the not-normalized
operator, our results extend those obtained in a previous work, where the
problem was solved under some geometrical restrictions on . In case of
the normalized operator, we also show that stadium-like domains are precisely
the unique convex sets in where the solution to a Dirichlet
problem is of class .Comment: 21 page
A regularity result for the inhomogeneous normalized infinity Laplacian
We prove that the unique solution to the Dirichlet problem with constant
source term for the inhomogeneous normalized infinity Laplacian on a convex
domain of is of class . The result is obtained by showing
as an intermediate step the power-concavity (of exponent ) of the
solution.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1410.611
Optimal partitions for Robin Laplacian eigenvalues
We prove the existence of an optimal partition for the multiphase shape
optimization problem which consists in minimizing the sum of the first Robin
Laplacian eigenvalue of mutually disjoint {\it open} sets which have a
-countably rectifiable boundary and are contained into a
given box in $R^d
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