Monotone operators in divergence form with $x$-dependent multivalued graphs

Gilles Francfort; François Murat; Luc Tartar

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Displaying similar documents to “Monotone operators in divergence form with $x$ -dependent multivalued graphs”

On the existence of viable solutions for a class of second order differential inclusions

Aurelian Cernea (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We prove the existence of viable solutions to the Cauchy problem x” ∈ F(x,x’), x(0) = x₀, x’(0) = y₀, where F is a set-valued map defined on a locally compact set $M \subset R^{2 n}$ , contained in the Fréchet subdifferential of a ϕ-convex function of order two.

Hysteresis filtering in the space of bounded measurable functions

Pavel Krejčí, Philippe Laurençot (2002)

Bollettino dell'Unione Matematica Italiana

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We define a mapping which with each function $u \in L^{\infty} (0, T)$ and an admissible value of $r > 0$ associates the function $ξ$ with a prescribed initial condition $ξ^{0}$ which minimizes the total variation in the $r$ -neighborhood of $u$ in each subinterval $[0, t]$ of $[0, T]$ . We show that this mapping is non-expansive with respect to $u$ , $r$ and $ξ^{0}$ , and coincides with the so-called play operator if $u$ is a regulated function.

Can we assign the Borel hulls in a monotone way?

Márton Elekes, András Máthé (2009)

Fundamenta Mathematicae

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A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ $G_{δ}$ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone $G_{δ}$ hull operation for all measurable sets is consistent. It remains open whether existence here is also...

Existence for implicit differential equations in Banach spaces

Viorel Barbu, Angelo Favini (1992)

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

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We prove two existence results on abstract differential equations of the type $d (B u) / d t + A (u) = f$ and we give some applications of them to partial differential equations.

Nonlinear multivalued boundary value problems

Ralf Bader, Nikolaos S. Papageorgiou (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when $d o m A \neq ℝ^{N}$ and $d o m A = ℝ^{N}$ , with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.

Homogenization of some nonlinear problems with specific dependence upon coordinates

P. Courilleau, S. Fabre, J. Mossino (2001)

Bollettino dell'Unione Matematica Italiana

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Questo articolo considera una successione di equazioni differenziali a derivate parziali non lineari in forma di divergenza del tipo $- div (Q^{ϵ} G (x, N^{ϵ} \nabla u)) = f^{ϵ},$ in un dominio limitato $Ω$ dello spazio $n$ -dimensionale; $Q^{ϵ} = Q^{ϵ} (x)$ e $N^{ϵ} = N^{ϵ} (x)$ sono matrici con coefficenti limitati, $N^{ϵ}$ e è invertibile e la sua matrice inversa $R^{ϵ}$ ha anche coefficenti limitati. La non linearità è dovuta alla funzione $G = G (x, ξ)$ ; la condizione di crescita, la monotonicità e le ipotesi di coercitività sono modellate sul $p$ -Laplaciano, $1 < p < \infty$ , ed assicurano l'esistenza di...

Monotone extenders for bounded c-valued functions

Kaori Yamazaki (2010)

Studia Mathematica

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Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, $C_{\infty} (A, c)$ the set of all bounded continuous functions f: A → c, and $C_{A} (X, c)$ the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender $u : C_{\infty} (A, c) \to C_{A} (X, c)$ . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer...

Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions

Sahbi Boussandel (2018)

Applications of Mathematics

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The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet $p$ -Laplace operator.

Displaying similar documents to “Monotone operators in divergence form with x -dependent multivalued graphs”

Displaying similar documents to “Monotone operators in divergence form with $x$ -dependent multivalued graphs”