Liouville type condition and the interior regularity of quasilinear parabolic system (the case of BMO-solutions)

Jana Stará; Josef Daněček; Oldřich John

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Displaying similar documents to “Liouville type condition and the interior regularity of quasilinear parabolic system (the case of BMO-solutions)”

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Oldřich John (1982)

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 We prove a $C^{k, α}$ partial regularity result for local minimizers of variational integrals of the type $I (u) = \int_{Ω} f (D^{k} u (x)) d x$ , assuming that the integrand satisfies growth conditions. 

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We derive local a priori estimates of the Hölder norm of solutions to quasilinear elliptic systems with quadratic nonlinearities in the gradient. We assume higher integrability of solutions and smallness of its BMO norm but the Hölder norm is estimated in terms of BMO norm of the solution under consideration, only.

On weak Hessian determinants

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Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.