Enea Parini

Continuity of the variational eigenvalues of the p-Laplacian with respect to p

In this note it is shown that a result of Champion and De Pascale [‘Asymptotic behavior of nonlinear eigenvalue problems involving p-Laplacian type operators’, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 1179–1195] implies that the variational eigenvalues of the p-Laplacian are continuous with respect to p.

The Second Eigenvalue of thep-Laplacian aspGoes to1

The asymptotic behaviour of the second eigenvalue of the -Laplacian operator as goes to 1 is investigated. The limit setting depends only on the geometry of the domain. In the particular case of a planar disc, it is possible to show that the second eigenfunctions are nonradial if is close enough to 1.

On the positivity preserving property of hinged plates

In this work we show that the Kirchhoff–Love model for a hinged plate

On the existence threshold for positive solutions of p-Laplacian equations with a concave–convex nonlinearity

\Delta^2 v = f \text{ in }E,\; v = \Delta v - (1 - \sigma) \kappa v_n = 0 \text{ on }\partial E

On the Moser–Trudinger inequality in fractional Sobolev–Slobodeckij spaces

admits, for

A free boundary approach to the Rosensweig instability of ferrofluids

f \in L^2(E)

On multiplicity of eigenvalues and symmetry of eigenfunctions of the

and

p

-1 < \sigma < 1

-Laplacian

, a unique weak solution in

The second eigenvalue of the p-Laplacian as p goes to 1

W^{2,2}(E) \cap W^{1,2}_0(E)