# Poincarï¿½ inequality and Palaisï¿½Smale condition for the p-Laplacian

## Related Articles

- The Second Eigenvalue of the p-Laplacian as p Goes to 1. Parini, Enea // International Journal of Differential Equations;2010, p1
The asymptotic behaviour of the second eigenvalue of the p-Laplacian operator as p 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 p is close...

- OPTIMIZATION IN PROBLEMS INVOLVING THE P-LAPLACIAN. MARRAS, MONICA // Electronic Journal of Differential Equations;2010, Vol. 2010, Special section p1
We minimize the energy integral âˆ«Î© |âˆ‡u|p dx, where g is a bounded positive function that varies in a class of rearrangements, p > 1, and u is a solution of -Î”pu = g in Î© u = 0 on âˆ‚Î©. Also we maximize the first eigenvalue Î» = Î»g, where -Î”pu = Î»gup-1 in...

- Deleting vertices and interlacing Laplacian eigenvalues. Baofeng WU; Jiayu SHAO; Xiying YUAN // Chinese Annals of Mathematics;Mar2010, Vol. 31 Issue 2, p231
The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G - U, which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edges. Also, some applications of this interlacing property are explored and...

- GENERALIZED PICONE AND RICCATI INEQUALITIES FOR HALF-LINEAR DIFFERENTIAL OPERATORS WITH ARBITRARY ELLIPTIC MATRICES. FIŠNAROVÁ, SIMONA; MAŘÍK, ROBERT // Electronic Journal of Differential Equations;2010, Vol. 2010, Special section p1
In the article, we extend the well-known Picone identity for half-linear partial differential equations to equations with anisotropic p-Laplacian.

- Fluctuations of eigenvalues and second order PoincarÃ© inequalities. Chatterjee, Sourav // Probability Theory & Related Fields;Jan2009, Vol. 143 Issue 1/2, p1
Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in question. In this article we attempt to formulate a...

- Accuracy of the difference scheme of solving the eigenvalue problem for the Laplacian. Maiko, N.; Prikazchikov, V.; Ryabichev, V. // Cybernetics & Systems Analysis;Sep2011, Vol. 47 Issue 5, p783
The finite-difference approximation of the eigenvalue problem with the Dirichlet boundary conditions for the Laplacian in a two-dimensional domain of complex form is analyzed for accuracy and the error of eigenfunctions from the class $ W_2^2\left( \Omega \right) $ in the mesh norm of $...

- On the nodal sets of toral eigenfunctions. Bourgain, Jean; Rudnick, Ze�v // Inventiones Mathematicae;Jul2011, Vol. 185 Issue 1, p199
We study the nodal sets of eigenfunctions of the Laplacian on the standard d-dimensional flat torus. The question we address is: Can a fixed hypersurface lie on the nodal sets of eigenfunctions with arbitrarily large eigenvalue? In dimension two, we show that this happens only for segments of...

- WEIGHTED EIGENVALUE PROBLEMS FOR THE p-LAPLACIAN WITH WEIGHTS IN WEAK LEBESGUE SPACES. ANOOP, T. V. // Electronic Journal of Differential Equations;2011, Vol. 2011, Special section p1
We consider the nonlinear eigenvalue problem -Î”pu = Î»g|u|p-2u, u âˆˆ DÂ¹0,1,p(Î© ) where Î”p is the p-Laplacian operator, Î© is a connected domain in RN with N > p and the weight function g is locally integrable. We obtain the existence of a unique positive principal...

- Effects of confinement on the order-disorder transition of diblock copolymer melts. Bing Miao; Dadong Yan; Han, Charles C.; An-Chang Shi // Journal of Chemical Physics;4/14/2006, Vol. 124 Issue 14, p144902
The effects of confinement on the order-disorder transition of diblock copolymer melts are studied theoretically. Confinements are realized by restricting diblock copolymers in finite spaces with different geometries (slabs, cylinders, and spheres). Within the random phase approximation, the...