Estimates for the first eigenvalue for p-Laplacian with mixed boundary conditions

THE FIRST EIGENVALUE OF p-LAPLACIAN SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS

ISOLATION AND SIMPLICITY FOR THE FIRST EIGENVALUE OF THE p-LAPLACIAN WITH A NONLINEAR BOUNDARY CONDITION

Here Ω is a bounded domain in RN with smooth boundary, ∆pu = div(|∇u|p−2∇u) is the p-Laplacian, and ∂/∂ν is the outer normal derivative. In the linear case, that is for p = 2, this eigenvalue problem is known as the Steklov problem (see [3]). Problems of the form (1.1) appear in a natural way when one considers the Sobolev trace inequality. In fact, the immersionW1,p(Ω) ↪→ Lp(∂Ω) is compact, he...

An Isoperimetric Inequality for the Second Eigenvalue of the Laplacian with Robin Boundary Conditions

We prove that the second eigenvalue of the Laplacian with Robin boundary conditions is minimised amongst all bounded Lipschitz domains of fixed volume by the domain consisting of the disjoint union of two balls of equal volume.

Existence solutions for new p-Laplacian fractional boundary value problem with impulsive effects

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

The ∞−Laplacian first eigenvalue problem

We review some results about the first eigenvalue of the infinity Laplacian operator and its first eigenfunctions in a general norm context. Those results are obtained in collaboration with several authors: V. Ferone, P. Juutinen and B. Kawohl (see [BFK], [BK1], [BJK] and [BK2]). In section 5 we make some remarks on the simplicity of the first eigenvalue of ∆∞: this will be the object of a join...