Summary: Acta Math. Univ. Comenianae
Vol. LXVI, 2(1997), pp. 321--328
A FUJITA--TYPE THEOREM FOR THE LAPLACE EQUATION
WITH A DYNAMICAL BOUNDARY CONDITION
H. AMANN and M. FILA
Abstract. We find a critical exponent for global existence of positive solutions of
the Laplace equation on a halfspace with a dynamical boundary condition.
Given a nonempty open subset X of R m we denote by BUC(X) the Banach
space of all bounded and uniformly continuous functions on X , endowed with the
supremum norm k \Delta k1 . We also put BUC+ (X) := \Phi
u 2 BUC(X) ; u(x) – 0 for
x 2 X
. Moreover, H n := R n\Gamma1 \Theta (0; 1) is the open upper halfspace in R n , and
its boundary @H n is identified with R n\Gamma1 .
We fix q 2 (1; 1) and consider the following system:
\Deltau = 0