Continuity for bounded solutions of multiphase Stefan problem

Emmanuele DiBenedetto; Vincenzo Vespri

Displaying similar documents to “Continuity for bounded solutions of multiphase Stefan problem”

Parabolic equations with multiple singularities

Di Benedetto, Emmanuele

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Boundary estimates for certain degenerate and singular parabolic equations

Benny Avelin, Ugo Gianazza, Sandro Salsa (2016)

Journal of the European Mathematical Society

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We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic $p$ -Laplacian equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part $S_{T}$ of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of...

Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms

Rabah Mecheter, Fares Mokhtari (2023)

Mathematica Bohemica

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In this paper, we study the existence results for some parabolic equations with degenerate coercivity, singular lower order term depending on the gradient, and positive initial data in $L^{1}$ .

Estimates of Green functions and their applications for parabolic operators with singular potentials

Lotfi Riahi (2003)

Colloquium Mathematicae

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We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a $C^{1, 1}$ cylindrical domain Ω. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.

Cauchy-Dirichlet problem in Morrey spaces for parabolic equations with discontinuous coefficients

Dian K. Palagachev, Maria A. Ragusa, Lubomira G. Softova (2003)

Bollettino dell'Unione Matematica Italiana

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Let $Q_{T}$ be a cylinder in $R^{n + 1}$ and $x = (x^{'}, t) \in R^{n} \times R$ . It is studied the Cauchy-Dirichlet problem for the uniformly parabolic operator $\{\begin{matrix} u_{t} - \overset{n}{\sum_{i, j = 1}} a^{i j} (x) D_{i j} u = f (x) & q.o. in Q_{T}, \\ u (x) = 0 & su \partial Q_{T}, \end{matrix}$ in the Morrey spaces $W_{p, λ}^{2, 1} (Q_{T})$ , $p \in (1, \infty)$ , $λ \in (0, n + 2)$ , supposing the coefficients to belong to the class of functions with vanishing mean oscillation. There are obtained a priori estimates in Morrey spaces and Hölder regularity for the solution and its spatial derivatives.

Estimates of weak solutions to nondiagonal quasilinear parabolic systems

Dmitry Portnyagin (2005)

Annales Polonici Mathematici

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$L^{\infty}$ -estimates of weak solutions are established for a quasilinear non-diagonal parabolic system with a special structure whose leading terms are modelled by p-Laplacians. A generalization of the weak maximum principle to systems of equations is employed.

The Wolff gradient bound for degenerate parabolic equations

Tuomo Kuusi, Giuseppe Mingione (2014)

Journal of the European Mathematical Society

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The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of $p$ -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.