id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-320	Hafeez, Usman; Lavier, Theo; Williams, Lucas; Korobenko, Lyudmila	Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators	2021	19	.pdf	application/pdf	7614	388	76	Let u be a weak solution to (1.1) on Ω = B and define u+ = max{u, 0}, then the following Caccioppoli inequality holds on the ball B∫ {x∈B:u(x)>0} |∇Au+|2 dµ ≤ ∫ {x∈B:u(x)>0} u+‖f‖L∞ dµ, where dµ = dx|B|. Proof. Moreover, if the above estimate holds for q = σ′ then Sobolev inequality (1.2) holds (almost necessity).	cache/ejde-320.pdf	txt/ejde-320.txt