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Titlebook: Geometric Properties for Parabolic and Elliptic PDE‘s; Rolando Magnanini,Shigeru Sakaguchi,Angelo Alvino Book 2013 Springer-Verlag Italia

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Measurements on High-Temperature SteelsLet .:=−.+. be a critical Schrödinger operator on ..(..), where .≥3 and . is a radially symmetric function decaying quadratically at the space infinity. We study the optimal decay rate of the operator norm of the Schrödinger heat semigroup .. from ..(..) to ..(..) (2≤.≤∞).
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Conference proceedings 20081st editionA regular variation of a bounded domain in the Euclidean space is considered. The perturbation formula for the eigenvalue of an operator arising in the Maxwell equation under this type of domain variation is given.
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Metal Housing with Magnetic MaterialsIn this paper, we obtain a mountain pass characterization of ground state solutions for some class of elliptic equations in ℝ. with nonlinearities in the critical (exponential) growth range.
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Power Concavity for Solutions of Nonlinear Elliptic Problems in Convex Domains,We investigate convexity properties of solutions to elliptic Dirichlet problems in convex domains. In particular we give conditions on the operator . such that a suitable power of a positive solution . of a fully nonlinear equation .(.,.,.,...)=0 in a convex domain ., vanishing on ., is concave.
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Geometric Analysis of Fractional Phase Transition Interfaces,We discuss some recent results on phase transition models driven by nonlocal operators, also in relation with their limit (either local or nonlocal) interfaces.
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