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- W4294022403 abstract "Let $u: Omega subseteq mathbb{R}^n longrightarrow mathbb{R}^N$ be a smooth map and $n,N in mathbb{N}$. The $infty$-Laplacian is the PDE system [ tag{1} label{1} Delta_infty u , :=, Big(Du otimes Du + |Du|^2[Du]^bot! otimes IBig) :D^2u, =, 0, ] where $[Du]^bot := text{Proj}_{R(Du)^bot}$. eqref{1} constitutes the fundamental equation of vectorial Calculus of Variations in $L^infty$, associated to the model functional [ tag{2} label{2} E_infty (u,Omega'), =, big| |Du|^2big|_{L^infty(Omega')} , Omega' Subset Omega. ] We show that generalised solutions to eqref{1} can be characterised in terms of eqref{2} via a set of designated affine variations. For the scalar case $N=1$, we utilise the theory of viscosity solutions of Crandall-Ishii-Lions. For the vectorial case $Ngeq 2$, we utilise the recently proposed by the author theory of $mathcal{D}$-solutions. Moreover, we extend the result described above to the $p$-Laplacian, $1<p<infty$." @default.
- W4294022403 created "2022-09-01" @default.
- W4294022403 creator A5041596758 @default.
- W4294022403 date "2015-09-06" @default.
- W4294022403 modified "2023-10-14" @default.
- W4294022403 title "A New Characterisation of $infty$-Harmonic and $p$-Harmonic Maps via Affine Variations in $L^infty$" @default.
- W4294022403 doi "https://doi.org/10.48550/arxiv.1509.01811" @default.
- W4294022403 hasPublicationYear "2015" @default.
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