Improved resolvent estimates for constant-coefficient elliptic operators\n in three dimensions

2021/01/01 by Robert Schippa, Schippa, Robert
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2105.02270

openalex publication_date 2021/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove new L^p-L^q-estimates for solutions to elliptic differential\noperators with constant coefficients in \ℝ³. We use the estimates\nfor the decay of the Fourier transform of particular surfaces in \ℝ³\nwith vanishing Gaussian curvature due to Erd Hos--Salmhofer to derive new\nFourier restriction--extension estimates. These allow for constructing\ndistributional solutions in L^q(\ℝ³) for L^p-data via limiting\nabsorption by well-known means.\n

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