Displaying similar documents to “The microstructure of Lipschitz solutions for a one-dimensional logarithmic diffusion equation”

Higher order linear connections from first order ones

Włodzimierz M. Mikulski (2007)

Archivum Mathematicum

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We describe how find all ℳ f m -natural operators D transforming torsion free classical linear connections ∇ on m -manifolds M into r -th order linear connections D ( ∇ ) on M .

On the eigenvalues of a Robin problem with a large parameter

Alexey Filinovskiy (2014)

Mathematica Bohemica

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We consider the Robin eigenvalue problem Δ u + λ u = 0 in Ω , ∂ u / ∂ ν + α u = 0 on ∂ Ω where Ω ⊂ ℝ n , n ≥ 2 is a bounded domain and α is a real parameter. We investigate the behavior of the eigenvalues λ k ( α ) of this problem as functions of the parameter α . We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative λ 1 ' ( α ) . Assuming that the boundary ∂ Ω is of class C 2 we obtain estimates to the difference λ k D - λ k ( α ) between the k -th eigenvalue of the Laplace operator with...

Lattice effect algebras densely embeddable into complete ones

Zdena Riečanová (2011)

Kybernetika

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An effect algebraic partial binary operation ø p l u s defined on the underlying set E uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion E ^ of E there exists an effect algebraic partial binary operation ⊕ ^ then ⊕ ^ need not be an extension of ⊕ . Moreover, for an Archimedean atomic lattice effect algebra E we give a necessary and sufficient condition for that ⊕ ^ existing on E ^ is an extension of ⊕ defined on E . Further we show that such ⊕ ^ extending ⊕ exists...

A β -normal Tychonoff space which is not normal

Eva Murtinová (2002)

Commentationes Mathematicae Universitatis Carolinae

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α -normality and β -normality are properties generalizing normality of topological spaces. They consist in separating dense subsets of closed disjoint sets. We construct an example of a Tychonoff β -normal non-normal space and an example of a Hausdorff α -normal non-regular space.

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let D be a nonempty compact subset of a Banach space X and denote by S ( X ) the family of all nonempty bounded closed convex subsets of X . We endow S ( X ) with the Hausdorff metric and show that there exists a set ℱ ⊂ S ( X ) such that its complement S ( X ) ∖ ℱ is σ -porous and such that for each A ∈ ℱ and each x ˜ ∈ D , the set of solutions of the best approximation problem ∥ x ˜ - z ∥ → min , z ∈ A , is nonempty and compact, and each minimizing sequence has a convergent subsequence.