In this talk, I will describe a new approach to general relativistic initial data gluing based on explicit solution operators for the linearized constraint equation with prescribed support properties. In particular, we retrieve and optimize -- in terms of positivity, regularity, size and/or spatial decay requirements -- obstruction-free gluing originally put forth by Czimek-Rodnianski. Notably, our proof of the strengthened obstruction-free gluing theorem relies on purely spacelike techniques, rather than null gluing as in the original approach.

In this talk, we will discuss nonlocal elliptic and parabolic equations on C^{1,τ} open sets in weighted Sobolev spaces, where τ ∈ (0, 1). The operators we consider are infinitesimal generators of symmetric stable Levy processes, whose Levy measures are allowed to be very singular. Additionally, for parabolic equations, the measures are assumed to be merely measurable in the time variable. This talk is based on a joint work with Hongjie Dong (Brown University).

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ID: 853 0775 9189, PW: 342420