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Zeitschrift für Analysis und ihre Anwendungen


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Volume 40, Issue 3, 2021, pp. 261–276
DOI: 10.4171/ZAA/1684

Published online: 2021-04-19

Existence of Solutions to the $A$-Laplace System via Young Measures

Farah Balaadich[1] and Elhoussine Azroul[2]

(1) Université Sidi Mohamed Ben Abdellah, Fès, Morocco
(2) Université Sidi Mohamed Ben Abdellah, Fès, Morocco

We study the existence of solutions for the $A$-Laplace system of the form $$ \left\{\begin{aligned} -\Delta_Au&=f &&\text{in}\ \Omega,\\ u&=0 && \text{on}\ \partial\Omega, \end{aligned}\right. $$ where $-\Delta_A u:=-\operatorname{div}(a(\lvert Du\rvert)Du)$. The existence result is proved by using the technique of Young measures.

Keywords: $A$-Laplacian systems, Orlicz–Sobolev spaces, weak solutions, Young measures

Balaadich Farah, Azroul Elhoussine: Existence of Solutions to the $A$-Laplace System via Young Measures. Z. Anal. Anwend. 40 (2021), 261-276. doi: 10.4171/ZAA/1684