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

Hemoptysis

https://doi.org/10.1007/978-1-4842-2623-0ase with small initial data in weighted ..-spaces. This problem in multidimensional cases was dealt with in Sobajima (Differ Integr Equ 32:615–638, 2019) via the weighted Hardy inequality which is false in one-dimension. The crucial idea of the proof is the use of an incomplete version of Hardy ineq

凹处

https://doi.org/10.1007/978-3-030-73363-6Elliptic equations; Parabolic equations; Functional and isoperimetric inequalities; Overdetermined and

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矛盾

,Wave–Particle Duality in Quantum Optics,This note deals with a one-dimensional quasilinear chemotaxis system. The first part summarizes recent results, in which a new energy-like functional is introduced and plays a key role. In the latter half, the energy-like functional will be derived in a more general situation.

CANDY

https://doi.org/10.1007/978-94-007-2404-4Solvability of semilinear heat equations with general nonlinearity is investigated. Applying a quasi scale invariant transformation, we clarify the threshold singularity of initial data for existence and nonexistence results.

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白杨

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Foam-Cells

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A Note on Radial Solutions to the Critical Lane-Emden Equation with a Variable Coefficient,In this note, we consider the following problem . where . ≥ 3 and . is the unit ball centered at the origin and .(.) is a radial Hölder continuous function such that .(0) = 0. We prove the existence and nonexistence of radial solutions by the variational method with the concentration compactness analysis and the Pohozaev identity.