Viscosity Solutions and Viscosity Subderivatives in Smooth Banach Spaces with Applications to Metric Regularity
Copyright policy )Viscosity Solutions and Viscosity Subderivatives in Smooth Banach Spaces with Applications to Metric Regularity
Let \(X\) be a real Banach space endowed with a bornology \(\beta\). If \(f:X\to[-\infty,+ \infty]\) is lower semicontinuous and \(f(x)<+\infty\), the authors define the notion of \(\beta\)-viscosity subderivative of \(f\) at \(x\). For such a notion, refined versions of ``fuzzy'' sum rules are proved. They allow the authors to establish a quite general uniqueness result for the viscosity solutions of Hamilton-Jacobi equations in Banach spaces. As a further application, a unified treatment of metric regularity is also provided.
- University of Newcastle Australia Australia
- Simon Fraser University Canada
subderivatives, viscosity solutions, fuzzy sum rule, Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games, Nonsmooth analysis, viscosity subderivative, Fréchet and Gateaux differentiability in optimization, smooth spaces, fuzzy sum, 510, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Hamilton–Jacobi equations, metric regularity, Hamilton-Jacobi equations in Banach spaces
subderivatives, viscosity solutions, fuzzy sum rule, Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games, Nonsmooth analysis, viscosity subderivative, Fréchet and Gateaux differentiability in optimization, smooth spaces, fuzzy sum, 510, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, Hamilton–Jacobi equations, metric regularity, Hamilton-Jacobi equations in Banach spaces
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