Compactness methods for $\Gamma^{1,\alpha}$ boundary Schauder estimates in Carnot groups

Agnid Banerjee; Isidro Munive; Nicola Garofalo

arxiv: 1804.06697 · v2 · pith:ZPTJI36Onew · submitted 2018-04-18 · 🧮 math.AP

Compactness methods for Gamma^(1,α) boundary Schauder estimates in Carnot groups

Agnid Banerjee , Nicola Garofalo , Isidro Munive This is my paper

classification 🧮 math.AP

keywords alphaboundarygammacarnotestimatesgroupsschaudercompactness

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The aim of this paper is to prove $\Gamma^{1,\alpha}$ Schauder estimates near a $C^{1,\alpha}$ non-characteristic portion of the boundary for $\Gamma^{0, \alpha}$ perturbations of horizontal Laplaceans in Carnot groups. This situation of minimally smooth domains presents itself naturally in the study of subelliptic free boundary problems of obstacle type, see [15].

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Compactness methods for Gamma^(1,α) boundary Schauder estimates in Carnot groups

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