Second order parabolic systems, optimal regularity, and singular sets of solutions

Frank Duzaar; Giuseppe Mingione

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Regularity results for parabolic systems related to a class of non-newtonian fluids

E Acerbi, G Mingione, G. A. Seregin (2004)

Annales de l'I.H.P. Analyse non linéaire

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Solutions of nonlinear parabolic equations without growth restrictions on the data.

Boccardo, Lucio, Gallouët, Thierry, Vazquez, Juan Luis (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Existence and nonexistence of global solutions of the quasilinear parabolic equations with inhomogeneous terms.

Kobayashi, Yasumaro (2010)

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The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation

Jiaqing Pan (2011)

Open Mathematics

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In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.

On Hölder regularity for vector-valued minimizers of quasilinear functionals

Josef Daněček, Eugen Viszus (2010)

Mathematica Bohemica

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We discuss the interior Hölder everywhere regularity for minimizers of quasilinear functionals of the type $𝒜 (u; Ω) = \int_{Ω} A_{i j}^{α β} (x, u) D_{α} u^{i} D_{β} u^{j} d x$ whose gradients belong to the Morrey space $L^{2, n - 2} (Ω, ℝ^{n N})$ .

A fundamental estimate and an inequality of Caccioppoli's type for nonlinear parabolic systems of higher order

Roberto Amato (1991)

Czechoslovak Mathematical Journal

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