TY  - JOUR
ID  - ElBahja2023
LB  - ElBahja2023
AU  - El Bahja, Hamid
TI  - Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions
ST  - Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 6
SP  - 759
EP  - 788
DO  - https://doi.org/10.7494/OpMath.2023.43.6.759
UR  - https://doi.org/10.7494/OpMath.2023.43.6.759
AB  - We study the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations driven by nonstandard \(p(x,t),q(x,t)\)-growth condition. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time \(L^{\infty}\) bounds for the weak solutions.
KW  - existence theory
KW  - nonlinear parabolic problems
KW  - nonstandard growth
KW  - regularity theory
SN  - 1232-9274
ER  -