Affiliation:
1. Istituto Lombardo - Sapienza Università di Roma, P.le A. Moro 2, 00185, Roma, Italy
2. Dipartimento di Matematica, Sapienza Università di Roma, P.le A. Moro 2, 00185, Roma, Italy
Abstract
<p style='text-indent:20px;'>In this paper we prove, using a duality method, existence of solutions for the nonlinear elliptic mean field games type system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left\{ \begin{array}{cl} -{\mathop{{{\rm{div}}}}}(M(x)\,{\nabla} u) + u - {\mathop{{{\rm{div}}}}}(u\,A(x)\,{\nabla}\psi) = f(x) & {\rm{in \; \Omega ,}}\\ -{\mathop{{{\rm{div}}}}}(M(x)\,{\nabla}\psi) + \psi + A(x)\,{\nabla}\psi \cdot {\nabla} \psi = u^{p-1} & {\rm{in \; \Omega ,}} \\ u = 0 = \psi & {\rm{on \; \partial\Omega ,}} \end{array} \right. $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>under different assumptions on <inline-formula><tex-math id="M1">\begin{document}$ p > 1 $\end{document}</tex-math></inline-formula>, and the function <inline-formula><tex-math id="M2">\begin{document}$ f(x) $\end{document}</tex-math></inline-formula> in Lebesgue spaces.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Analysis,General Medicine
Reference21 articles.
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