Mappings of generalized finite distortion and continuity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475605" target="_blank" >RIV/00216208:11320/23:10475605 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rixOG_SXFt" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rixOG_SXFt</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.12835" target="_blank" >10.1112/jlms.12835</a>
Alternative languages
Result language
angličtina
Original language name
Mappings of generalized finite distortion and continuity
Original language description
We study continuity properties of Sobolev mappings f is an element of W-loc(1,n )(Omega,R-n),n >= 2, that satisfy the following generalized finite distortion inequality|Df(x)}(n ) <= K(x) J(f)(x)+Sigma(x)for almost every x is an element of R-n. Here K: Omega -> [1,infinity) and Sigma: Omega -> [0,infinity) are measurable functions. Note that when Sigma equivalent to 0, we recover the class of mappings of finite distortion, which are always continuous. The continuity of arbitrary solutions, however, turns out to be an intricate question. We fully solve the continuity problem in the case of bounded distortion K is an element of L-infinity(Omega), where a sharp condition for continuity is that Sigma is in the Zygmund space Sigma log(mu)(e+Sigma)is an element of L-loc(1)(Omega) for some mu > n-1. We also show that one can slightly relax the boundedness assumption on K to an exponential class exp (lambda K) is an element of L-loc(1)(Omega) with lambda > n+1, and still obtain continuous solutions when Sigma log(mu)(e+Sigma)is an element of L-loc(1)(Omega) with mu>lambda. On the other hand, for all p,q is an element of[1,infinity] with p(-1)+q(-1)=1, we construct a discontinuous solution with K is an element of L-loc(p)(Omega) and Sigma/K is an element of L-loc(q)(Omega), including an example with Sigma is an element of L-loc(infinity)(Omega) and K is an element of L-loc(1)(Omega).
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of the London Mathematical Society
ISSN
0024-6107
e-ISSN
1469-7750
Volume of the periodical
1
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
37
Pages from-to
1-37
UT code for WoS article
001104130200001
EID of the result in the Scopus database
2-s2.0-85176767860