In this article, we are interested in an initial value optimal control problem for a evolutionary p-Laplace equation driven by multiplicative Lévy noise. We first present wellposedness of a weak solution by using an implicit time discretization of the problem, along with the Jakubowski version of the Skorokhod theorem for a non-metric space. We then formulate associated control problem, and establish existence of an optimal solution by using variational method and exploiting the convexity property of the cost functional.
Keywords: Evolutionary $p$-Laplace equation, stochastic PDEs, weak solution, Skorokhod theorem
@article{COCV_2020__26_1_A100_0,
author = {Majee, Ananta K.},
title = {Stochastic optimal control of a evolutionary $p${-Laplace} equation with multiplicative {L\'evy} noise},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2020},
publisher = {EDP Sciences},
volume = {26},
doi = {10.1051/cocv/2020028},
mrnumber = {4185059},
zbl = {1465.45010},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2020028/}
}
TY - JOUR AU - Majee, Ananta K. TI - Stochastic optimal control of a evolutionary $p$-Laplace equation with multiplicative Lévy noise JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2020028/ DO - 10.1051/cocv/2020028 LA - en ID - COCV_2020__26_1_A100_0 ER -
%0 Journal Article %A Majee, Ananta K. %T Stochastic optimal control of a evolutionary $p$-Laplace equation with multiplicative Lévy noise %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2020028/ %R 10.1051/cocv/2020028 %G en %F COCV_2020__26_1_A100_0
Majee, Ananta K. Stochastic optimal control of a evolutionary $p$-Laplace equation with multiplicative Lévy noise. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 100. doi: 10.1051/cocv/2020028
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