Trudinger's inequality for double phase functionals with variable exponents

Fumi-Yuki Maeda; Yoshihiro Mizuta; Takao Ohno; Tetsu Shimomura

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 2, page 511-528
  • ISSN: 0011-4642

Abstract

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Our aim in this paper is to establish Trudinger’s inequality on Musielak-Orlicz-Morrey spaces L Φ , κ ( G ) under conditions on Φ which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger’s inequality for double phase functionals Φ ( x , t ) = t p ( x ) + a ( x ) t q ( x ) , where p ( · ) and q ( · ) satisfy log-Hölder conditions and a ( · ) is nonnegative, bounded and Hölder continuous.

How to cite

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Maeda, Fumi-Yuki, et al. "Trudinger's inequality for double phase functionals with variable exponents." Czechoslovak Mathematical Journal 71.2 (2021): 511-528. <http://eudml.org/doc/298274>.

@article{Maeda2021,
abstract = {Our aim in this paper is to establish Trudinger’s inequality on Musielak-Orlicz-Morrey spaces $L^\{\Phi ,\kappa \}(G)$ under conditions on $\Phi $ which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger’s inequality for double phase functionals $\Phi (x,t) = t^\{p(x)\} + a(x) t^\{q(x)\}$, where $p(\cdot )$ and $q(\cdot )$ satisfy log-Hölder conditions and $a(\cdot )$ is nonnegative, bounded and Hölder continuous.},
author = {Maeda, Fumi-Yuki, Mizuta, Yoshihiro, Ohno, Takao, Shimomura, Tetsu},
journal = {Czechoslovak Mathematical Journal},
keywords = {Riesz potential; Trudinger's inequality; Musielak-Orlicz-Morrey space; double phase functional},
language = {eng},
number = {2},
pages = {511-528},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Trudinger's inequality for double phase functionals with variable exponents},
url = {http://eudml.org/doc/298274},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Maeda, Fumi-Yuki
AU - Mizuta, Yoshihiro
AU - Ohno, Takao
AU - Shimomura, Tetsu
TI - Trudinger's inequality for double phase functionals with variable exponents
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 511
EP - 528
AB - Our aim in this paper is to establish Trudinger’s inequality on Musielak-Orlicz-Morrey spaces $L^{\Phi ,\kappa }(G)$ under conditions on $\Phi $ which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger’s inequality for double phase functionals $\Phi (x,t) = t^{p(x)} + a(x) t^{q(x)}$, where $p(\cdot )$ and $q(\cdot )$ satisfy log-Hölder conditions and $a(\cdot )$ is nonnegative, bounded and Hölder continuous.
LA - eng
KW - Riesz potential; Trudinger's inequality; Musielak-Orlicz-Morrey space; double phase functional
UR - http://eudml.org/doc/298274
ER -

References

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