The Poincaré Inequality Does Not Improve with Blow-Up

Andrea Schioppa

Displaying similar documents to “The Poincaré Inequality Does Not Improve with Blow-Up”

A note on the Poincaré inequality

Alireza Ranjbar-Motlagh (2003)

Studia Mathematica

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The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.

Nonexistence of minimal blow-up solutions of equations $i u_{t} = - Δ u - k (x) {| u |}^{4 / N} u$ in $ℝ^{N}$

Franck Merle (1996)

Annales de l'I.H.P. Physique théorique

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Poincaré's inequality and global solutions of a nonlinear parabolic equation

Philippe Souplet, Fred B. Weissler (1999)

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A note on global integrability of upper gradients of p-superharmonic functions

Outi Elina Maasalo, Anna Zatorska-Goldstein (2009)

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We consider a complete metric space equipped with a doubling measure and a weak Poincaré inequality. We prove that for all p-superharmonic functions there exists an upper gradient that is integrable on H-chain sets with a positive exponent.

Liouville theorems and blow up behaviour in semilinear reaction diffusion systems

D. Andreucci, M. A. Herrero, J. J. L. Velázquez (1997)

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Recent progress on the blow-up problem of Zakharov equations

Frank Merle (1995)

Journées équations aux dérivées partielles

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Decay and asymptotic behavior of solutions of the Keller-Segel system of degenerate and nondegenerate type

Takayoshi Ogawa (2006)

Banach Center Publications

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We classify the global behavior of weak solutions of the Keller-Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.

Asymptotics for $L^{2}$ minimal blow-up solutions of critical nonlinear Schrödinger equation

Frank Merle (1996)

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Similarity stabilizes blow-up

Steve Schochet (1999)

Journées équations aux dérivées partielles

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The blow-up of solutions to a quasilinear heat equation is studied using a similarity transformation that turns the equation into a nonlocal equation whose steady solutions are stable. This allows energy methods to be used, instead of the comparison principles used previously. Among the questions discussed are the time and location of blow-up of perturbations of the steady blow-up profile.

A description of self-similar blow-up for dimensions $n \geq 3$

J. Bebernes, D. Eberly (1988)

Annales de l'I.H.P. Analyse non linéaire

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