Andrea Pinamonti, Simone Verzellesi, Changyou Wang
Published 2022-02-28Version 1
Given a $C^2$ family of vector fields $X_1,...,X_m$ which induces a continuous Carnot-Carath\'eodory distance, we show that any absolute minimizer of a supremal functional defined by a $C^2$ quasiconvex Hamiltonian $f(x, z, p)$, allowing $z$-variable dependence, is a viscosity solution to the Aronsson equation $-\langle X(f(x, u(x), Xu(x))), D_p f(x, u(x), Xu(x))\rangle = 0.$
Endpoint Sobolev inequalities for vector fields and cancelling operators
Nonlocal criteria for compactness in the space of $L^{p}$ vector fields
Well-posedness for the continuity equation for vector fields with suitable modulus of continuity
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