Solomon George Meyers 1897–1965

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A Note on Meyers’ Theorem in W

Lower semicontinuity properties of multiple integrals u ∈W (Ω;R) 7→ ∫ Ω f(x, u(x), · · · ,∇u(x)) dx are studied when f may grow linearly with respect to the highest-order derivative, ∇ku, and admissible W k,1(Ω;Rd) sequences converge strongly in W k−1,1(Ω;Rd). It is shown that under certain continuity assumptions on f, convexity, 1-quasiconvexity or k-polyconvexity of ξ 7→ f(x0, u(x0), · · · ,∇...

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Let M be a complete Riemannian manifold and D ⊂ M a smoothly bounded domain with compact closure. We use Brownian motion and the classic results on the Stieltjes moment problem to study the relationship between the Dirichlet spectrum of D and the heat content asymptotics of D. Central to our investigation is a sequence of invariants associated to D defined using exit time moments. We prove that...

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ژورنال

عنوان ژورنال: Gastroenterology

سال: 1966

ISSN: 0016-5085

DOI: 10.1016/s0016-5085(66)80084-7