The Aronsson equation for absolute minimizers of $L^\infty$-functionals associated with vector fields satisfying Hörmander's condition

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dc.creatorWang, Changyou
dc.date2003-07-14
dc.date.accessioned2026-07-07T04:59:39Z
dc.date.available2026-07-07T04:59:39Z
dc.descriptionGiven a Carnot-Carathéodory metric space $(R^n, d_{\hbox{cc}})$ generated by vector fields $\{X_i\}_{i=1}^m$ satisfying Hörmander's condition, we prove in theorem A that any absolute minimizer $u\in W^{1,\infty}_{\hbox{cc}}(\Om)$ to $F(v,\Om)=\sup_{x\in\Om}f(x,Xv(x))$ is a viscosity solution to the Aronsson equation (1.6), under suitable conditions on $f$. In particular, any AMLE is a viscosity solution to the subelliptic $\infty$-Laplacian equation (1.7). If the Carnot-Carathédory space is a Carnot group ${\bf G}$ and $f$ is independent of $x$-variable, we establish in theorem C the uniquness of viscosity solutions to the Aronsson equation (1.13) under suitable conditions on $f$. As a consequence, the uniqueness of both AMLE and viscosity solutions to the subelliptic $\infty$-Laplacian equation is established in ${\bf G}$
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0307198
dc.identifierhttp://arxiv.org/abs/math/0307198
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68074
dc.subjectAnalysis of PDEs
dc.subject35J70; 49L25; 49J40
dc.titleThe Aronsson equation for absolute minimizers of $L^\infty$-functionals associated with vector fields satisfying Hörmander's condition
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