On the asymptotic behavior of solutions of quasilinear elliptic equations
Lancaster, Kirk E. Stanley, Jeremy
Lancaster, Kirk E.
Stanley, Jeremy
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2003-01-01
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Article
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Keywords
Phragmèn-Lindelöf theorem,Behavior at infinity,Degenerate elliptic equation,Elliptic equation,Parabolic equation
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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.
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Springer-Verlag
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Annali dell'Universita di Ferrara;v.49 no.1
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0365-7833