# Tangent lines of contact for the infinity Laplacian

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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...

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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.

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In this paper, we investigate the existence of weak quasi-periodic solutions for the second order Hamiltonian system with damped term: Ã¼(t) + q(t)Ã¼ (t) + DW(u(t)) = 0, t âˆˆ R, (HSD) where u : R â†’ Rn, q : R â†’ R is a quasi-periodic function, W : Rn â†’ R is...

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Finite subset spaces of a metric space $X$ form a nested sequence under natural isometric embeddings $X=X(1)\subset X(2)\subset \cdots \,$. We prove that this sequence admits Lipschitz retractions $X(n)\rightarrow X(n-1)$ when $X$ is a Hilbert space.

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We study the Maximum Principle and existence of positive weak solutions for the nÃ—n nonlinear elliptic system (Multiple line equation(s) cannot be represented in ASCII text) where the degenerated p-Laplacian defined as Î”P,pu = div [P(x)âˆ£âˆ‡uâˆ£p-2âˆ‡u] with p > 1,...

- Backward Stochastic Differential Equations in Infinite Dimensions with Continuous Driver and Applications. Fuhrman, Marco; Hu, Ying // Applied Mathematics & Optimization;Sep2007, Vol. 56 Issue 2, p265
In this paper we prove the existence of a solution to backward stochastic differential equations in infinite dimensions with continuous driver under various assumptions. We apply our results to a stochastic game problem with infinitely many players.