We study the asymptotic behavior as $\lambda\rightarrow 0^+$ of $\lambda v_\lambda$, where $v_\lambda$ is the viscosity solution of the following Hamilton-Jacobi-Isaacs equation (infinite horizon case) $$ \lambda v_\lambda + H(x,Dv_\lambda)=0, $$ with $$ H(x,p):=\min_{b\in B}\max_{a \in A} \{-f(x,a,b)\cdot p -l(x,a,b)\}. $$ We discuss the case in which the state of the system is required to stay in the closure of a bounded domain $\Omega\subset{\Bbb R}^n$ with sufficiently smooth boundary (for example $\partial \Omega\in {\cal C}^2$). Under the uniform approximate controllability assumption of one player, we extend the convergence result of the term $\lambda v_\lambda (x)$ to a constant as $\lambda\rightarrow 0^+$ to Differential Games . We also show how to contruct nonanticipative strategies which satisfies some "good" estimates in order to obtain Holder regularity of the value function.
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Water waves
Research Group:
Speaker:
L. Biasco,
Institution:
University Roma 3
Schedule:
Wednesday, December 3, 2003 - 06:00 to 07:00
Location:
room L
Abstract:
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Jinpeng Lu
On the stability of Gel'fand's inverse problem
Wednesday, February 19, 2025 - 14:00
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Wei Cheng
Singularity Propagation: Dynamic and Transport Perspectives
Wednesday, February 26, 2025 - 14:00 to 15:00
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Daniel Hernández Ruipérez
Algebraic supergeometry and moduli of stable supermaps
Thursday, February 27, 2025 - 16:00
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Growth of Sobolev norms for completely resonant quantum Harmonic Oscillators in R2
Saturday, December 13, 2025 - 14:00
Today's Lectures
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09:00 to 11:00
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