Geodesic
Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky--Meyers estimate
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 3-22

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous $p(\,\cdot\,)$-Laplace equation with a variable exponent $p$ having a logarithmic continuity modulus.
Keywords: Zaremba problem, Meyers estimates, capacity, embedding theorems, higher integrability. 
@article{TMF_2024_218_1_a0,
     author = {Yu. A. Alkhutov and G. A. Chechkin},
     title = {Multidimensional {Zaremba} problem for the $p(\,\cdot\,)$-laplace equation. {A} {Boyarsky--Meyers} estimate},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--22},
     publisher = {mathdoc},
     volume = {218},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a0/}
}
TY  - JOUR
AU  - Yu. A. Alkhutov
AU  - G. A. Chechkin
TI  - Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky--Meyers estimate
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2024
SP  - 3
EP  - 22
VL  - 218
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a0/
LA  - ru
ID  - TMF_2024_218_1_a0
ER  - 
%0 Journal Article
%A Yu. A. Alkhutov
%A G. A. Chechkin
%T Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky--Meyers estimate
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2024
%P 3-22
%V 218
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a0/
%G ru
%F TMF_2024_218_1_a0
Yu. A. Alkhutov; G. A. Chechkin. Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky--Meyers estimate. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 3-22. http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a0/