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Nonconvex Optimal Control Problems with Nonsmooth Mixed State
Nonconvex Optimal Control Problems with Nonsmooth Mixed State

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On Malliavin`s proof of Hörmander`s theorem

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... In particular, f is not continuous on either of the sets [0, 1] nor [0, ∞) and hence the convergence can not be uniform on either of these sets by Theorem 24.3. 24.7 Let fn (x) = x − xn for x ∈ [0, 1]. (a) Does the sequence (fn ) converge pointwise on the set [0, 1]? If so, give the limit function. ...
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Measures and functions in locally convex spaces Rudolf Gerrit Venter

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Sobolev space

In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, thus a Banach space. Intuitively, a Sobolev space is a space of functions with sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function.Sobolev spaces are named after the Russian mathematician Sergei Sobolev. Their importance comes from the fact that solutions of partial differential equations are naturally found in Sobolev spaces, rather than in spaces of continuous functions and with the derivatives understood in the classical sense.
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