 
Summary: Acta Math. Univ. Comenianae
Vol. LXVI, 2(1997), pp. 321328
321
A FUJITATYPE 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.
1. Introduction
Given a nonempty open subset X of Rm
we denote by BUC(X) the Banach
space of all bounded and uniformly continuous functions on X, endowed with the
supremum norm · . We also put BUC+(X) := u BUC(X) ; u(x) 0 for
x X . Moreover, Hn
:= Rn1
× (0, ) is the open upper halfspace in Rn
, and
its boundary Hn
is identified with Rn1
.
