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A bound for the solutions of a basic elliptic system with non-linearity q 2

Sergio Campanato (1986)

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

In questa Nota si dimostra un risultato enunciato nel § 5 della pubblicazione [4]. Per le soluzioni di un sistema ellittico base, con non-linearità q 2 , vale un principio di massimo analogo a quello dimostrato in [3] nel caso di non-linearità q = 2 .

A gradient estimate for solutions of the heat equation. II

Charles S. Kahane (2001)

Czechoslovak Mathematical Journal

The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.

A maximum principle for systems with variational structure and an application to standing waves

Nicholas D. Alikakos, Giorgio Fusco (2015)

Journal of the European Mathematical Society

We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.

A parabolic quasilinear problem for linear growth functionals.

Fuensanta Andreu, Vincent Caselles, José María Mazón (2002)

Revista Matemática Iberoamericana

We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth.

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