We deal with a class of nondivergence type elliptic and parabolic equations degenerating at the coordinate hyperplanes. Assuming that the degeneration is coordinatewise and varies regularly, we prove the Hölder continuity of solutions. Also, the approximative solutions are considered. §

Abstract Let f : X → be an invertible Lipschitz transformation on a compact metric space . Given Hölder continuous operator cocycles Banach and -invariant ergodic measure, this paper establishes the continuity of Oseledets subspaces over set arbitrarily large measure. This extends result in [V Araujo, A I Bufetov S Filip, On Hölder-continuity subspaces, J. Lond. Math. Soc. 2016, 93 194–218]. fo...

We examine the regularity of weak solutions of quasi-geostrophic (QG) type equations with supercritical (α < 1/2) dissipation (−∆). This study is motivated by a recent work of Caffarelli and Vasseur, in which they study the global regularity issue for the critical (α = 1/2) QG equation [2]. Their approach successively increases the regularity levels of Leray-Hopf weak solutions: from L to L∞, f...