Czechoslovak Mathematical Journal, Vol. 55, No. 2, pp. 317-340, 2005

Boundedness of the solution of the third problem
for the Laplace equation

Dagmar Medkova

Mathematical Institute of the Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: medkova@math.cas.cz

Abstract: A necessary and sufficient condition for the boundedness of a solution of the third problem for the Laplace equation is given. As an application a similar result is given for the third problem for the Poisson equation on domains with Lipschitz boundary.

Keywords: third problem, Laplace equation

Classification (MSC 2000): 35B65, 35J05, 35J25, 31B10


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