The independence on p of pweak gradients is a classical problem in the Sobolev space metric theory. However, if no regularity assumption is enforced to the underlying space, the dependence of weak gradients on the integrable exponent is typically expected. In this seminar, we propose a new strategy based on optimal transportation techniques to achieve a strong kind of independence of pweak gradients on spaces satisfying Wasserstein interpolation L^{\infty}estimates. This improves previously available results in settings relying on Doubling & Poincarè assumptions. We push then this analysis to deduce fundamental information concerning the Sobolev and BV calculus on metric measure spaces. This is based on joint works with N. Gigli and E. Pasqualetto, T. Schultz.
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Progress on the independence on p of p weak gradients
Research Group:
Francesco Nobili
Institution:
SISSA
Schedule:
Friday, November 26, 2021  14:00
Location:
Online
Abstract:
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