Mapping Properties of Layer Potentials Associated with Higher-Order Elliptic Operators in Lipschitz Domains

Abstract

The method of layer potentials has been applied with tremendous success in the treatment of boundary value problems for second-order differential operators for a very long time; the literature on this topic is enormous. By way of contrast this method is disproportionally underdeveloped in the case of higher-order operators; the difference between the higher-order and the second-order settings is striking in term of the scientific output. This paper presents new results which establish mapping properties of multiple layer potentials associated with higher-order elliptic operators in Lipschitz domains in ℝ n .