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- W4287979072 abstract "We study the elliptic inclusion given in the following divergence form begin{align*} & -mathrm{div}, A(x,nabla u) ni fquad mathrm{in}quad Omega, & u=0quad mathrm{on}quad partial Omega. end{align*} As we assume that $fin L^1(Omega)$, the solutions to the above problem are understood in the renormalized sense. We also assume nonstandard, possibly nonpolynomial, heterogeneous and anisotropic growth and coercivity conditions on the maximally monotone multifunction $A$ which necessitates the use of the nonseparable and nonreflexive Musielak--Orlicz spaces. We prove the existence and uniqueness of the renormalized solution as well as, under additional assumptions on the problem data, its relation to the weak solution. The key difficulty, the lack of a Carath'{e}odory selection of the maximally monotone multifunction is overcome with the use of the Minty transform." @default.
- W4287979072 created "2022-07-26" @default.
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- W4287979072 date "2019-12-29" @default.
- W4287979072 modified "2023-10-16" @default.
- W4287979072 title "On renormalized solutions to elliptic inclusions with nonstandard growth" @default.
- W4287979072 doi "https://doi.org/10.48550/arxiv.1912.12729" @default.
- W4287979072 hasPublicationYear "2019" @default.
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