# Large solutions to the p-Laplacian for large p

## Related Articles

- Optimal regularity for the pseudo infinity Laplacian. Julio Rossi; Mariel Saez // ESAIM: Control, Optimisation & Calculus of Variations;Apr2007, Vol. 13 Issue 2, p294
In this paper we find the optimal regularity for viscositysolutions of the pseudo infinity Laplacian. We prove that thesolutions are locally Lipschitz and show an example that provesthat this result is optimal. We also show existence and uniquenessfor the Dirichlet problem.

- THE EXISTENCE OF MULTIPLE SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS. JIAQUAN LIU; SHIBO LIU // Bulletin of the London Mathematical Society;Aug2005, Vol. 37 Issue 4, p592
Using Morse theory and the truncation technique, a proof is given of the existence of at least three nontrivial solutions for a class of $p$-Laplacian equations. When $p=2$, the existence of four nontrivial solutions is also considered.

- Viscosity solutions methods for converse KAM theory. Diogo Gomes; Adam Oberman // ESAIM: Mathematical Modelling & Numerical Analysis;Nov2008, Vol. 42 Issue 6, p1047
The main objective of this paper is to prove new necessary conditions to the existence of KAM tori. To do so, we develop a set of explicit a-priori estimates for smooth solutions of Hamilton-Jacobi equations, using a combination of methods from viscosity solutions, KAM and Aubry-Mather theories....

- Viscosity solution of nonanticipating Hamilton-Jacobi equations. Lukoyanov, N. // Differential Equations;Dec2007, Vol. 43 Issue 12, p1715
The article discusses the Hamilton-Jacobi functional equation under the satisfying and Lipschitz condition. It examines the generalized solutions of Hamilton-Jacobi equations and the partial differential equations of the first and second order and determines the two approaches such as a minimax...

- Tangent lines of contact for the infinity Laplacian. Yu, Yifeng // Calculus of Variations & Partial Differential Equations;Dec2004, Vol. 21 Issue 4, p349
In this paper, we will prove a â€œtangent line touchingâ€ condition for supersolutions of the infinity Laplacian. This is a kind of quantitative estimate for the failure of the strong maximal principle. Whenn= 2, this also implies the failure of the principle of unique continuation. In...

- Biased tug-of-war, the biased infinity Laplacian, and comparison with exponential cones. Peres, Yuval; Pete, Gábor; Somersille, Stephanie // Calculus of Variations & Partial Differential Equations;Jul2010, Vol. 38 Issue 3/4, p541
We prove that if $${U\subset \mathbb {R}^n}$$ is an open domain whose closure $${\overline U}$$ is compact in the path metric, and F is a Lipschitz function on âˆ‚ U, then for each $${\beta \in \mathbb {R}}$$ there exists a unique viscosity solution to the Î²-biased infinity Laplacian...

- The infinity Laplacian in infinite dimensions. Gaspari, Thierry // Calculus of Variations & Partial Differential Equations;Nov2004, Vol. 21 Issue 3, p243
We study three properties of real-valued functions defined on a Banach space: The absolutely minimizing Lipschitz functions, the viscosity solutions of the infinity Laplacian partial differential equation, and the functions which satisfy comparison with cones. We prove that these notions are...

- Representation Formulas for Solutions of the HJI Equations with Discontinuous Coefficients and Existence of Value in Differential Games. GARAVELLO, M.; SORAVIA, P. // Journal of Optimization Theory & Applications;Aug2006, Vol. 130 Issue 2, p209
In this paper, we study the Hamilton-Jacobi-Isaacs equation of zerosum differential games with discontinuous running cost. For such class of equations, the uniqueness of the solutions is not guaranteed in general. We prove principles of optimality for viscosity solutions where one of the players...

- Multiplicity of solutions for anisotropic quasilinear elliptic equations with variable exponents. Stancu-Dumitru, Denisa // Bulletin of the Belgian Mathematical Society - Simon Stevin;Dec2010, Vol. 17 Issue 5, p875
We study an anisotropic partial differential equation on a bounded domain Î© âŠ‚ RN. We prove the existence of at least two nontrivial weak solutions using as main tools themountain pass lemma and Ekeland's variational principle.