A Smooth Variational Principle with Applications to Hamilton-Jacobi Equations in Infinite Dimensions

✍ Scribed by R. Deville; G. Godefroy; V. Zizler

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 557 KB
• Volume: 111
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1993.1009

✦ Synopsis

We prove that if (X) is a Banach space which admits a smooth Lipschitzian bump function. then for every lower semicontinuous bounded below function (f), there exists a Lipschitzian smooth function (g) on (X) such that (f+g) attains its strong minimum on (X), thus extending a result of Borwein and Preiss. We then show how the above result can be used io obtain existence and uniqueness results of viscosity solutions of Hamilton-Jacobi equations in infinite dimensional Banach spaces without assuming the Radon Nikodym property: 199: Academic Prens. Inc