An explicit form for extremal functions in the embedding constant problem for Sobolev spaces

DOI10.1090/mosc/292zbMath1451.46038arXiv2001.00245OpenAlexW3014574672MaRDI QIDQ4960303

T. A. Garmanova, I. A. Sheipak

Publication date: 14 April 2020

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.00245

zbMATH Keywords

Sobolev spacesLegendre polynomialsembedding constants

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (3)

Relationship between the best \(L_p\) approximations of splines by polynomials with estimates of the values of intermediate derivatives in Sobolev spaces ⋮ On sharp estimates of even-order derivatives in Sobolev spaces ⋮ Estimates of derivatives in Sobolev spaces in terms of hypergeometric functions

Cites Work

• On properties of integrals of the Legendre polynomial
• Sharp estimates for derivatives of functions in the Sobolev classes \(\overset{\circ} {W}_{2}^r (-1,1)\)
• On the symmetry of extremal in several embedding theorems
• Unnamed Item

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