2019/10/15 by Emma-Karoliina Kurki, Kurki, Emma-Karoliina, Antti V. Vähäkangas +1
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1910.06839
We prove a local two-weight Poincar 'e inequality for cubes using the sparse\ndomination method that has been influential in harmonic analysis. The proof\ninvolves a localized version of the Fefferman--Stein inequality for the sharp\nmaximal function. By establishing a local-to-global result in a bounded domain\nsatisfying a Boman chain condition, we show a two-weight p-Poincar 'e\ninequality in such domains. As an application we show that certain nonnegative\nsupersolutions of the p-Laplace equation and distance weights are\np-admissible in a bounded domain, in the sense that they support versions of\nthe p-Poincar 'e inequality.\n