OPTIMAL SOBOLEV TRACE EMBEDDINGS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10337160" target="_blank" >RIV/00216208:11320/16:10337160 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/tran/6606" target="_blank" >http://dx.doi.org/10.1090/tran/6606</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/tran/6606" target="_blank" >10.1090/tran/6606</a>

Result language
angličtina
Original language name
OPTIMAL SOBOLEV TRACE EMBEDDINGS
Original language description
Optimal target spaces are exhibited in arbitrary-order Sobolev type embeddings for traces of n-dimensional functions on lower dimensional subspaces. Sobolev spaces built upon any rearrangement-invariant norm are allowed. A key step in our approach consists of showing that any trace embedding can be reduced to a one-dimensional inequality for a Hardy type operator depending only on n and on the dimension of the relevant subspace. This can be regarded as an analogue for trace embeddings of a well-known symmetrization principle for first-order Sobolev embeddings for compactly supported functions. The stability of the optimal target space under iterations of Sobolev trace embeddings is also established and is part of the proof of our reduction principle. As a consequence, we derive new trace embeddings, with improved (optimal) target spaces, for classical Sobolev, Lorentz-Sobolev and Orlicz-Sobolev spaces.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)