ANTI-MAXIMUM PRINCIPLES

GUIDO SWEERS

G.H.Sweers@its.tudelft.nl

Dept. of Applied Mathematical Analysis

ITS Faculty

Delft University of Technology

PO Box 5031, 2600 GA Delft, The Netherlands

ITS Faculty

Delft University of Technology

PO Box 5031, 2600 GA Delft, The Netherlands

For second order elliptic boundary value problems such as
in and on
it is
well known that for any reasonable bounded domain in
a first eigenvalue
exists and
moreover, for any
a positive source term
implies that the solution is positive. Clément and
Peletier showed that for in a right neighbourhood of
opposite behaviour occurs, an phenomenon which they named the *anti-maximum principle*: certain imply Such behaviour
is roughly explained by the pole of the resolvent at
and the positive sign of the corresponding eigenfunction

The anti-maximum principle for higher order elliptic boundary value problems
is joint work with Ph.Clément. Sharp conditions for the
uniform anti-maximum principle will appear in a joint work with
H.-Ch.Grunau.

EPSRC Gregynog Workshop, 21-26 July 2002