A new functional for the Calculus of Variations, involving the variational mean curvature of sets in $$R^n$$Rn
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DOI: 10.1007/s00229-017-0985-9
Abstract: We study the pth power $$W_p(E)=\int _{{\mathbb R}^n}|H_E|^p\,dx$$Wp(E)=∫Rn|HE|pdx, where $$H_E$$HE is the variational mean curvature of E, as defined in Barozzi (Rend Mat Acc Linceis 9(5):149–159, 1994) (see also in Proc Am Math Soc 99:313–316,… read more here.
Keywords: variational mean; mean curvature; functional calculus; new functional ... See more keywords
Functional calculus for generators of symmetric contraction semigroups
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DOI: 10.1215/00127094-3774526
Abstract: We prove that every generator of a symmetric contraction semigroup on a $\sigma$-finite measure space admits, for $1 read more here.
Keywords: contraction semigroups; generators symmetric; functional calculus; symmetric contraction ... See more keywords