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1994 | 108 | 1 | 5-20
Tytuł artykułu

Unique continuation for elliptic equations and an abstract differential inequality

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a class of elliptic equations whose leading part is the Laplacian and for which the singularities of the coefficients of lower order terms are described by a mixed $L^p$-norm. We prove that the zeros of the solutions are of at most finite order in the sense of a spherical L²-mean.
Słowa kluczowe
Czasopismo
Rocznik
Tom
108
Numer
1
Strony
5-20
Opis fizyczny
Daty
wydano
1994
otrzymano
1991-11-29
poprawiono
1992-11-23
Twórcy
autor
  • Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • [1] N. Aronszajn, A. Krzywicki and J. Szarski, A unique continuation theorem for exterior differential forms on Riemannian manifolds, Ark. Mat. 4 (1962), 417-453.
  • [2] B. Barcelo, C. E. Kenig, A. Ruiz and D. Sogge, Weighted Sobolev inequalities and unique continuation for the Laplacian plus lower order terms, Illinois J. Math. 32 (1988), 230-245.
  • [3] N. Garofalo and F. H. Lin, Monotonicity properties of variational integrals, $A_p$ weights and unique continuation, Indiana Univ. Math. J. 35 (1986), 245-268.
  • [4] N. Garofalo and F. H. Lin, Unique continuation for elliptic operators: a geometric-variational approach, Comm. Pure Appl. Math. 90 (1987), 347-366.
  • [5] L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. III, Springer, New York, 1985.
  • [6] L. Hörmander, Uniqueness theorems for second order elliptic differential equations, Comm. Partial Differential Equations 8 (1983), 21-64.
  • [7] D. Jerison, Carleman inequalities for the Dirac and Laplace operators and unique continuation, Adv. in Math. 62 (1986), 118-134.
  • [8] D. Jerison and C. E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. of Math. 121 (1985), 463-488.
  • [9] J. L. Kazdan, Unique continuation in geometry, Comm. Pure Appl. Math. 91 (1988), 667-681.
  • [10] C. E. Kenig, Restriction theorems, Carleman estimates, uniform Sobolev inequalities and unique continuation, in: Lecture Notes in Math. 1384, Springer, 1989, 69-90.
  • [11] Y. M. Kim, MIT thesis, 1989.
  • [12] P. D. Lax, A stability theorem for solutions of abstract differential equations, and its application to the study of the local behaviour of solutions of elliptic equations, Comm. Pure Appl. Math. 9 (1956), 747-766.
  • [13] F. H. Lin, A uniqueness theorem for parabolic equations, Comm. Pure Appl. Math. 93 (1990), 127-136.
  • [14] A. Pliś, On non-uniqueness in Cauchy problem for an elliptic second order differential equation, Bull. Acad. Polon. Sci. 11 (1963), 95-100.
  • [15] R. T. Seeley, Singular integrals on compact manifolds, Amer. J. Math. 81 (1959), 658-690.
  • [16] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1) (1965), 189-258.
  • [17] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
  • [18] R. Strichartz, Multipliers for spherical harmonic expansions, Trans. Amer. Math. Soc. 167 (1972), 115-124.
  • [19] T. H. Wolff, Unique continuation for |Δu| ≤ V|∇u| and related problems, Rev. Mat. Iberoamericana 6 (1990), 155-200.
  • [20] T. H. Wolff, A property of measures in $ℝ^n$ and an application to unique continuation, preprint.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv108i1p5bwm
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