Resumen de The annular decay property and capacity estimates for thin annuli

Anders Björn, Jana Björn, Juha Lehrbäck

• We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted ?? and in metric spaces, primarily under the assumptions of an annular decay property and a Poincaré inequality. In particular, if the measure has the 1-annular decay property at ?0 and the metric space supports a pointwise 1-Poincaré inequality at ?0 , then the upper and lower bounds are comparable and we get a two-sided estimate for thin annuli centred at ?0 . This generalizes the known estimate for the usual variational capacity in unweighted ?? . We also characterize the 1-annular decay property and provide examples which illustrate the sharpness of our results.