On the asymptotic behavior of solutions of quasilinear elliptic equations

No Thumbnail Available
Authors
Lancaster, Kirk E.
Stanley, Jeremy
Advisors
Issue Date
2003-01-01
Type
Article
Keywords
Phragmèn-Lindelöf theorem , Behavior at infinity , Degenerate elliptic equation , Elliptic equation , Parabolic equation
Research Projects
Organizational Units
Journal Issue
Citation
Lancaster, K. and J. Stanley. 2003. "On the asymptotic behavior of solutions of quasilinear elliptic equations." Annali dell'Universita di Ferrara 49(1): 85-125.
Abstract

The asymptotic behavior of solutions of second-order quasilinear elliptic and nonhyperbolic partial differential equations defined on unbounded domains in R n contained in {(Xl, ..., Xn): Ix,~ I < ~(~/x~ +... + x~_ 1)} for certain sublinear functions )~ is investigated when such solutions satisfy Dirichlet boundary conditions and the Dirichlet boundary data has appropriate asymptotic behavior at infinity. We prove Phragm~n-LindelSf theorems for large classes of nonhyperbolic operators, without ,lower order terms-, including uniformly elliptic operators and operators with well-defined genre, using special barrier functions which are constructed by considering an operator associated to our original operator. We also estimate the rate at which a solution converges to its limiting function at infinity in terms of properties of the top order coefficient ann of the operator and the rate at which the boundary values converge to their limiting function; these results are proven using appropriate barrier functions which depend on the behavior of the coefficients of the operator and the rate of convergence of boundary values.

Table of Contents
Description
Click on the link to access the article at the publisher's website (may not be free)
Publisher
Springer-Verlag
Journal
Book Title
Series
Annali dell'Universita di Ferrara;v.49 no.1
PubMed ID
DOI
ISSN
0365-7833
EISSN