Displaying similar documents to “Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients.”

How smooth is almost every function in a Sobolev space?

Aurélia Fraysse, Stéphane Jaffard (2006)

Revista Matemática Iberoamericana

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We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.

The Cauchy problem for viscous shallow water equations.

Weike Wang, Chao-Jiang Xu (2005)

Revista Matemática Iberoamericana

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In this paper we study the Cauchy problem for viscous shallow water equations. We work in the Sobolev spaces of index s > 2 to obtain local solutions for any initial data, and global solutions for small initial data.

Compact embeddings of Brézis-Wainger type.

Fernando Cobos, Thomas Kühn, Tomas Schonbek (2006)

Revista Matemática Iberoamericana

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Let Ω be a bounded domain in R and denote by id the restriction operator from the Besov space B (R) into the generalized Lipschitz space Lip(Ω). We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like e(id) ~ k if α > max (1 + 2/p + 1/q, 1/p). Our estimates improve previous results by Edmunds and Haroske.

Multipliers and weighted ∂ operator estimates.

Joaquim Ortega-Cerdà (2002)

Revista Matemática Iberoamericana

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We study estimates for the solution of the equation du=f in one variable. The new ingredient is the use of holomorphic functions with precise growth restrictions in the construction of explicit solution to the equation.

Solution to the gradient problem of C.E. Weil.

Zoltán Buczolich (2005)

Revista Matemática Iberoamericana

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In this paper we give a complete answer to the famous gradient problem of C. E. Weil. On an open set G ⊂ R we construct a differentiable function f: G → R for which there exists an open set Ω ⊂ R such that ∇f(p) ∈ Ω for a p ∈ G but ∇f(q) ∉ Ω for almost every q ∈ G. This shows that the Denjoy-Clarkson property does not hold in higher dimensions.