Revista Matemática Iberoamericana


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Volume 32, Issue 3, 2016, pp. 1001–1018
DOI: 10.4171/RMI/906

Published online: 2016-10-03

Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations

Olli Saari[1]

(1) Aalto University, Finland

We prove that local and global parabolic BMO spaces are equal thus extending the classical result of Reimann and Rychener. Moreover, we show that functions in parabolic BMO are exponentially integrable in a general class of space-time cylinders. As a corollary, we establish global integrability for positive supersolutions to a wide class of doubly nonlinear parabolic equations.

Keywords: Parabolic BMO, John–Nirenberg lemma, Hölder domain, quasihyperbolic boundary condition, doubly nonlinear equation, heat equation, global integrability

Saari Olli: Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations. Rev. Mat. Iberoamericana 32 (2016), 1001-1018. doi: 10.4171/RMI/906