Pointwise inequalities and approximation in fractional Sobolev spaces

• Autorzy: David Swanson
• Języki publikacji: EN

Abstrakty

EN

We prove that a function belonging to a fractional Sobolev space $L^{α,p}(ℝⁿ)$ may be approximated in capacity and norm by smooth functions belonging to $C^{m,λ}(ℝⁿ)$, 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].

Kategorie tematyczne

• 31B15: Potentials and capacities, extremal length
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section)
• 41A25: Rate of convergence, degree of approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 149
• Numer: 2
• Strony: 147-174

Daty

wydano

2002

Twórcy

autor

David Swanson

• Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A.

Identyfikatory

DOI

10.4064/sm149-2-5