The pseudo-$p$-Laplace eigenvalue problem and viscosity solutions as ${p\rightarrow \infty }$

Marino Belloni; Bernd Kawohl

Displaying similar documents to “The pseudo- $p$ -Laplace eigenvalue problem and viscosity solutions as $p \to \infty$ ”

Optimal regularity for the pseudo infinity Laplacian

Julio D. Rossi, Mariel Saez (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.

A remark on infinity harmonic functions.

Crandall, Michael G., Evans, L.C. (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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The application of Picone-type identity for some nonlinear elliptic differential equations.

Bognár, G., Došlý, O. (2003)

Acta Mathematica Universitatis Comenianae. New Series

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Relaxation of quasilinear elliptic systems via A-quasiconvex envelopes

Uldis Raitums (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the weak closure $W Z$ of the set $Z$ of all feasible pairs (solution, flow) of the family of potential elliptic systems where $Ω \subset 𝐑^{n}$ is a bounded Lipschitz domain, $F_{s}$ are strictly convex smooth functions with quadratic growth and $S = {σ m e a s u r a b l e ∣ σ_{s} (x) = 0 or 1, s = 1, \dots, s_{0}, σ_{1} (x) + \dots + σ_{s_{0}} (x) = 1}$ . We show that $W Z$ is the zero level set for an integral functional with the integrand $Q ℱ$ being the $𝐀$ -quasiconvex envelope for a certain function $ℱ$ and the operator $𝐀 = {(curl,div)}^{m}$ . If the functions $F_{s}$ are isotropic, then on the characteristic cone...

Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^{1} (Ω)$

M. F. Betta, A. Mercaldo, F. Murat, M. M. Porzio (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we prove uniqueness results for the renormalized solution, if it exists, of a class of non coercive nonlinear problems whose prototype is $\{\begin{matrix} - div (a (x) (1 + {| \nabla u |}^{2})^{\frac{p - 2}{2}} {\nabla u) + b (x) (1 + | \nabla u |}^{2})^{\frac{λ}{2}} = f & in Ω, \\ u = 0 & on \partial Ω, \end{matrix}$ where $Ω$ is a bounded open subset of $ℝ^{N}$ , $N \geq 2$ , $2 - 1 / N < p < N$ , $a$ belongs to $L^{\infty} (Ω)$ , $a (x) \geq α_{0} > 0$ , $f$ is a function in $L^{1} (Ω)$ , $b$ is a function in $L^{r} (Ω)$ and $0 \leq λ < λ^{*} (N, p, r),$ for some $r$ and $λ^{*} (N, p, r)$ .

A lower bound for the gradient of $\infty$ -harmonic functions.

Rosset, Edi (1996)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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A second eigenvalue bound for the Dirichlet-Schrödinger equation with a radially symmetric potential.

Haile, Craig (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper is devoted to the spectral analysis of a non elliptic operator $A$ , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator $A$ has been derived, we determine its continuous spectrum. Then, we show that $A$ is unbounded from below and that it has a sequence of negative eigenvalues tending to $- \infty$ . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization,...

Uniqueness of values of Aronsson operators and running costs in “tug-of-war” games

Yifeng Yu (2009)

Annales de l'I.H.P. Analyse non linéaire

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Displaying similar documents to “The pseudo- p -Laplace eigenvalue problem and viscosity solutions as p → ∞ ”

Displaying similar documents to “The pseudo- $p$ -Laplace eigenvalue problem and viscosity solutions as $p \to \infty$ ”