From affine Poincaré inequalities to affine spectral inequalities

Abstract: We develop the basic theory of $p$-Rayleigh quotients in bounded domains, in the affine case, for $p \geq 1$. We establish p-affine versions of the affine Poincaré inequality and introduce the affine invariant $p$-Laplace operator $\Delta_p^{\mathcal A}$ defining the Euler-Lagrange equation of the minimization problem. For $p=1$ we obtain the existence of affine Cheeger sets and study preliminary results towards a possible spectral characterization of John's position.

analysis of PDEsmetric geometry

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

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