Titlebook: Geometric Properties for Parabolic and Elliptic PDE‘s; Vincenzo Ferone,Tatsuki Kawakami,Futoshi Takahashi Book 2021 The Editor(s) (if appl

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Sharp Estimate of the Life Span of Solutions to the Heat Equation with a Nonlinear Boundary Conditiote by .(.) the life span of solutions to problem (P). We investigate the relationship between the singularity of . at the origin and .(.) for sufficiently large .?>?0 and the relationship between the behavior of . at the space infinity and .(.) for sufficiently small .?>?0. Moreover, we obtain shar

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Fabric

An Interpolating Inequality for Solutions of Uniformly Elliptic Equations,The Soap Bubble Theorem and Serrin’s problem: quantitative symmetry, PhD thesis, Università di Firenze, 2019), to the case of solutions of uniformly elliptic equations in divergence form, with merely measurable coefficients. The inequality for harmonic functions turned out to be a crucial ingredient

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Asymptotic Behavior of Solutions for a Fourth Order Parabolic Equation with Gradient Nonlinearity v as the ..-gradient flow for an energy functional which is unbounded from below. We first prove the existence and the uniqueness of solutions to the problem via the Galerkin method. Moreover, combining the potential well method with the Galerkin method, we study the asymptotic behavior of global-in-

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majestic

Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass,ondition introduced in the recent papers (Hirata and Tanaka, Adv Nonlinear Stud 19:263–290, 2019; Ikoma and Tanaka, Adv Differ Equ 24:609–646, 2019) and we prove the existence of a ground state solution for the nonlinear Choquard equation with prescribed mass, when . satisfies Berestycki-Lions type conditions.