Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators

DOI10.1215/S0012-7094-87-05518-9zbMath0644.35012MaRDI QIDQ1102436

Christopher D. Sogge, Alberto Ruiz, Carlos E. Kenig

Publication date: 1987

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationsunique continuationSobolev inequalitiessecond orderconstant coefficientCarleman inequalities

Mathematics Subject Classification ID

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• Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
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• Oscillatory integrals and spherical harmonics
• \(L^p-L^q\) estimates for the Klein-Gordon equation
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• A priori estimates for the wave equation and some applications
• Oscillatory integrals and multipliers on FL\(^p\)
• Uniqueness in Cauchy problems for differential equations with constant leading coefficients
• Uniqueness theorems for second order elliptic differential equations
• On Fourier coefficients and transforms of functions of two variables
• Oscillatory integrals and multiplier problem for the disc
• A restriction theorem for the Fourier transform

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