5 papers
On the relations between fundamental frequency and torsional rigidity in the case of anisotropic energies
Giuseppe Buttazzo, Raul Fernandes Horta
We consider variational energies of the form \[E_H(u)=\frac12\int_ΩH^2(\nabla u)\,dx\] defined on the Sobolev space , where is a general seminorm. Our primary objecti…
Sharp estimates for fundamental frequencies of elliptic operators generated by asymmetric seminorms in low dimensions
Julian Haddad, Raul Fernandes Horta, Marcos Montenegro
We establish new sharp asymmetric Poincare inequalities in one-dimension with the computation of optimal constants and characterization of extremizers. Using the one-dimensional th…
On the characterization of the Dirichlet and Fucik spectra of the one-dimensional anisotropic p-Laplace operator
Raul Fernandes Horta, Marcos Montenegro
The paper is concerned with the Dirichlet spectrum of the anisotropic -Laplace operator on an interval where \[ Δ^{a,b}_p u:= \left(a^{p…
On spectral optimization for p-Laplace type operators
Raul Fernandes Horta, Marcos Montenegro
Sharp uniform estimates, both lower and upper, are obtained for fundamental frequencies of -Laplace type operators generated by quadratic forms. Optimal constants are computed,…
Sharp isoanisotropic estimates for fundamental frequencies of membranes and connections with shapes
Raul Fernandes Horta, Marcos Montenegro
The underlying motivation of the present work lies on a cornerstone question in spectral optimization that consists of determining sharp lower and upper uniform estimates for funda…