5 papers
On the Hersch-Weinberger inequality in higher dimensions
T. V. Anoop, Vladimir Bobkov, Mrityunjoy Ghosh +1
We investigate a reverse Faber-Krahn type inequality for the Robin Laplacian in a bounded smooth domain whose boundary has two connected components. We pro…
On the nodal set conjecture for the -Laplacian in circularly symmetric domains
Vladimir Bobkov
In 1990, Pütter shown that the nodal line of any second eigenfunction of the Dirichlet Laplacian on a planar bounded simply connected domain intersects the boundary $\partial…
Reverse Faber-Krahn inequality for planar doubly connected domains
T. V. Anoop, Vladimir Bobkov, Mrityunjoy Ghosh
We prove that among all doubly connected and elastically supported planar membranes with prescribed values of the area and the lengths of the inner and outer boundaries…
Multiplicity of dead core solutions in indefinite elliptic problems
Vladimir Bobkov, Humberto Ramos Quoirin
We investigate nonnegative solutions of indefinite elliptic problems which enjoy the dead core phenomenon. Our model is the subhomogeneous problem $$ -Î_p u = (a^+(x) - μa^-(x))|…
Neumann domains of planar analytic eigenfunctions
T. V. Anoop, Vladimir Bobkov, Mrityunjoy Ghosh
Along with the partition of a planar bounded domain by the nodal set of a fixed eigenfunction of the Laplace operator in , one can consider another natural partition of $Î…