The Poincaré Inequality Does Not Improve with Blow-Up

Andrea Schioppa

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

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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.

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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.

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