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A REMARK ON UNIQUE CONTINUATION FOR THE CAUCHY-RIEMANN OPERATOR

서이혁
대한수학회 (The Korean Mathematical Society)|2015.09|대한수학회보 (Bulletin of the KMS)|제52권 제5호|pp. 1753-1757

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참고문헌

키워드

unique continuationCauchy-Riemann operator
주제분류수학

초록

In this note we obtain a unique continuation result for the differential inequality |∂u| ≤ |V u|, where ∂ = (i∂y + ∂x)/2 denotes the Cauchy-Riemann operator and V (x, y) is a function in L2(R2).

Abstract

In this note we obtain a unique continuation result for the differential inequality |∂u| ≤ |V u|, where ∂ = (i∂y + ∂x)/2 denotes the Cauchy-Riemann operator and V (x, y) is a function in L2(R2).

참고문헌 (10)

  1. T. Carleman, "Sur un probl`eme d’unicit´e pour les syst`emes d’´equations aux deriv´ees partielles `a deux variables ind´ependantes", Ark. Mat. Astr. Fys, 26(17), pp.1~9 (1939)
  2. L. Grafakos, "Classical Fourier Analysis" (2008), Springer
  3. D. Jerison, "Unique continuation and absence of positive eigenvalues for Schr¨odinger operators", Ann. of Math, 121(3), pp.463~494 (1985)
  4. C. E. Kenig, "Restriction theorems, Carleman estimates, uniform Sobolev inequalities and unique continuations, Harmonic analysis and partial differential equations (El Es-corial, 1987)", Lecture Notes in Math, 1384, pp.69~90 (1989), Springer
  5. C. E. Kenig, "A counterexample in unique continuation", Math. Res. Lett, 7(5-6), pp.625~630 (2000)
  6. C. E. Kenig, "Quantitative uniqueness estimates for second order elliptic equations with unbounded drift", Math. Res. Lett, 22(4), pp.1159~1175 (2015)
  7. H. Koch, "Sharp counterexamples in unique continuation for second order elliptic equations", J. Reine Angew. Math, 542, pp.133~146 (2002)
  8. N. Mandache, "A counterexample to unique continuation in dimension two", Comm. Anal. Geom, 10(1), pp.1~10 (2002)
  9. T. H. Wolff, "A property of measures in Rn and an application to unique continuation", Geom. Funct. Anal, 2(2), pp.225~284 (1992)
  10. T. H. Wolff, "Recent work on sharp estimates in second-order elliptic unique continuation problems", J. Geom. Anal, 3(6), pp.621~650 (1993)

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