Nearness of nonlinear operators

Fractional Klein-Gordon equation with singular mass. II: hypoelliptic case

“…This notion of "closeness", formally defined as nearness of operators, was developed to determine the well-posedeness of Dirichlet problems of non-linear elliptic equations, see e.g. [GT01], [DKY20], [BD02], [Ka17] in the Euclidean setting, where naturally the Laplacian should play the role of the operator to which close enough is the elliptic one. In the stratified case, see [DM05], the authors approximate the p-Laplacian on a bounded domain in the Heisenberg group H n by some non-homogeneous, noninvariant differential operator on H n .…”

“…The main result of this paper, see Theorem 1.5 below, concerns the well-posedeness of an equation with an associated differential operator expressed in terms of a function of the form a : G × R N 2 → R , for a stratified group G. This type of problem was previously considered in [DKY20, Theorem 3], where the authors also employ the method of nearness of operators, but in [DKY20] the space variable x lies in Ω, where Ω ⊂ R n is an open, bounded and convex domain of R n with a regular enough boundary. In this sense, our result is already new in the Euclidean setting.…”