On Liouville type theorems for second order elliptic differential equations

Lavi Karp

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1995)

  • Volume: 22, Issue: 2, page 275-298
  • ISSN: 0391-173X

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Karp, Lavi. "On Liouville type theorems for second order elliptic differential equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 22.2 (1995): 275-298. <http://eudml.org/doc/84206>.

@article{Karp1995,
author = {Karp, Lavi},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Fredholm operator; weighted Sobolev spaces},
language = {eng},
number = {2},
pages = {275-298},
publisher = {Scuola normale superiore},
title = {On Liouville type theorems for second order elliptic differential equations},
url = {http://eudml.org/doc/84206},
volume = {22},
year = {1995},
}

TY - JOUR
AU - Karp, Lavi
TI - On Liouville type theorems for second order elliptic differential equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1995
PB - Scuola normale superiore
VL - 22
IS - 2
SP - 275
EP - 298
LA - eng
KW - Fredholm operator; weighted Sobolev spaces
UR - http://eudml.org/doc/84206
ER -

References

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  1. [1] R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975. Zbl0314.46030MR450957
  2. [2] S. Agmon, On Positivity and decay of solutions of second order elliptic equations on Riemannian manifolds, Methods of Functional Analysis and Theory of Elliptic Equations (D. Greco ed.), Liguari Editore, Napoli, 1982, 19-52. Zbl0595.58044MR819005
  3. [3] M. Avellaneda - F.H. Lin, Une théorème de Liouville pour des équations elliptiques à coefficients périodiques, C. R. Acad. Sci. Paris Sér. I Math.309 (1989), 245-250. Zbl0691.35022MR1010728
  4. [4] M. Avellaneda - F.H. Lin, LP bounds on singular integrals in homogenization, Comm. Pure Appl. Math.44 (1991), 897-910. Zbl0761.42008MR1127038
  5. [5] H. Begehr - G.N. Hile, Schauder estimates and existence theory of entire solutions of linear elliptic operator, Proc. Roy. Soc. Edinburgh Sect. A110 (1988), 101-123. Zbl0674.35019MR963845
  6. [6] Yu. V. Egorov - M.A. Shubin, Linear Partial Differential Equations. Foundations of Classical Theory, Partial Differential Equations I (Yu. V. Egorov and M.A. Shubin, eds), Encyclopedia of Math. Sci., 30, Springer-Verlaga, Berlin-Heildelberg-New York, 1991. Zbl0738.35001MR1141631
  7. [7] A. Friedman, Bounded entire solutions of elliptic equations, Pacific J. Math.44 (1973), 497-507. Zbl0256.35024MR320506
  8. [8] L. Karp, Generalized Newton potential and its applications, J. Math. Anal. Appl.174 (1993), 480-497. Zbl0779.31004MR1215629
  9. [9] R.B. Lockhart, Fredholm properties of a class of elliptic operators on non-compact manifolds, Duke Math. J.48 (1981), 289-312. Zbl0486.35027MR610188
  10. [10] R.B. Lockhart - R.C. Mcowen, On elliptic system in Rn, Acta Math.150 (1983), 125-135. Zbl0517.35031MR697610
  11. [11] R.C. Mcowen, The behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math.32 (1979), 785-795. Zbl0426.35029MR539158
  12. [12] R.C. Mcowen, On elliptic operators in Rn, Comm. Partial Differential Equations5 (1980), 913-933. Zbl0448.35042MR584101
  13. [13] N. Meyers, An expansion about infinity for solutions of linear elliptic equations, J. Math. Mech.12 (1963), 247-264. Zbl0121.32202MR149072
  14. [14] C. Miranda, Partial Differential Equations of Elliptic Type, second edition, Springer-Verlag, Berlin-Heildelberg -New York, 1970. Zbl0198.14101MR284700
  15. [15] J. Moser - M. Struwe, On a Liouville type theorem for linear and nonlinear equations on a tours, Bol. Soc. Brasil. Mat.23 (1992), 1-20. Zbl0787.35028MR1203171
  16. [16] M. Murata, Isomorphism theorems for elliptic operators in Rn, Comm. Partial Differential Equations9 (1984), 1085-1105. Zbl0556.47027MR759238
  17. [17] M. Murata, On construction of Martin boundaries for second order elliptic equations, Publ. Res. Inst. Math. Sci.26 (1990), 585-627. Zbl0726.31009MR1081506
  18. [18] L. Nirenberg - H.F. Walker, The null spaces of elliptic partial differential operators in Rn, J. Math. Anal. Appl.42 (1973), 271-301. Zbl0272.35029MR320821
  19. [19] Y. Pinchover, On positive solutions of second second order elliptic equations, stability results and classification, Duke Math. J.57 (1988), 955-980. Zbl0685.35035MR975130
  20. [20] Y. Pinchover, On the equivalence Green functions of second order elliptic equations in Rn, Differential Integral Equation5 (1992), 481-493. Zbl0772.35015MR1157482
  21. [21] A. Pliś, A smooth linear elliptic differential equations without any solution in a sphere, Comm. Pure Appl. Math.14 (1961), 599-617. Zbl0163.13103MR136846
  22. [22] M. Schecter, Principles of Functional Analysis, Academic Press, New York, 1971. Zbl0211.14501MR445263
  23. [23] E. Stein - G. Weiss, Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, New Jersey, 1971. Zbl0232.42007MR304972

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