منابع مشابه
Structure Theory for Maximally Monotone Operators with Points of Continuity
In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of norm-to-weak∗ closedness and of property (Q) for these operators (as recently proven by Voisei). Various applications and limiting examples are given.
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In this paper we study homogenization of quasi-linear partial differential equations of the form −div (a (x, x/εh, Duh)) = fh on Ω with Dirichlet boundary conditions. Here the sequence (εh) tends to 0 as h → ∞ and the map a (x, y, ξ) is periodic in y, monotone in ξ and satisfies suitable continuity conditions. We prove that uh → u weakly in W 1,p 0 (Ω) as h → ∞, where u is the solution of a hom...
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Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. ...
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is called the effective domain of F, and F is said to be locally bounded at a point x e D(T) if there exists a neighborhood U of x such that the set (1.4) T(U) = (J{T(u)\ueU} is a bounded subset of X. It is apparent that, given any two monotone operators Tx and T2 from X to X*, the operator F», + T2 is again monotone, where (1 5) (Ti + T2)(x) = Tx(x) + T2(x) = {*? +x% I xf e Tx(x), xt e T2(x)}....
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1977
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1977-0425687-6