Integral representations and Liouville theorems for solutions of periodic elliptic equations Academic Article

abstract

• The paper contains integral representations for certain classes of exponentially growing solutions of second order periodic elliptic equations. These representations are the analogs of those previously obtained by S. Agmon, S. Helgason, and other authors for solutions of the Helmholtz equation. When one restricts the class of solutions further, requiring their growth to be polynomial, one arrives to Liouville type theorems, which describe the structure and dimension of the spaces of such solutions. The Liouville type theorems previously proved by M. Avellaneda and F.-H. Lin and J. Moser and M. Struwe for periodic second order elliptic equations in divergence form are significantly extended. Relations of these theorems with the analytic structure of the Fermi and Bloch surfaces are explained. 2001 Academic Press.

authors

• Kuchment, Peter

published proceedings

• JOURNAL OF FUNCTIONAL ANALYSIS

author list (cited authors)

• Kuchment, P.

citation count

• 19

complete list of authors

• Kuchment, P

publication date

• April 2001

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

keywords

• Elliptic Operator
• Floquet Theory
• Integral Representation
• Liouville Theorem
• Periodic Operator

Digital Object Identifier (DOI)

• 10.1006/jfan.2000.3727

start page

• 402

end page

• 446

volume

• 181

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1006%2Fjfan.2000.3727