Inside a fixed bounded domain $\Omega $ of the plane, we look for the best compact
connected set $ K $, of given perimeter, in order to maximize the first Dirichlet eigenvalue …

We study the regularity and topological structure of a compact connected set S minimizing
the “compliance" functional with a length penalization. The compliance here is the work of …

The primary objective of this paper is to establish the Ahlfors regularity of minimizers of set
functions that satisfy a suitable maxitive condition on disjoint unions of sets. Our analysis …

We study a shape optimization problem for the first eigenvalue of an elliptic operator in
divergence form, with nonconstant coefficients, over a fixed domain Ω. Dirichlet conditions …

This book provides an introduction to the broad topic of the calculus of variations. It
addresses the most natural questions on variational problems and the mathematical …

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Account Menu Find a journal Publish with us Track your research Search Cart Book cover A …

These lecture notes give an overview of “isoperimetric inequalities”, namely inequalities
involving only geometric features, for the eigenvalues of the Laplace operator, with Dirichlet …

We look for best partitions of the unit interval that minimize certain functionals defined in
terms of the eigenvalues of Sturm–Liouville problems. Via Γ-convergence theory, we study …

Calculus of Variations — Upscaling of screw dislocations with increasing tangen- tial strain, by
Ilaria Lucardesi, Marco Moran Page 1 Rend. Lincei Mat. Appl. 31 (2020), 421–445 DOI …

We investigate the dependence of optimal constants in Poincaré–Sobolev inequalities of
planar domains on the region where the Dirichlet condition is imposed. More precisely, we …