Session S38 - Geometric Potential Analysis

Friday, July 16, 19:35 ~ 20:05 UTC-3

From affine Poincaré inequalities to affine spectral inequalities

Julián Haddad

UFMG, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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.

Joint work with Marcos Montenegro (UFMG, Brazil) and Hugo Jiménez (PUC-Rio, Brazil).

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