Interior L_p-estimates for functions with integral representations

Abstract

For fnctions having either boundary integral representations or domain integral representations the present paper proves apriori estimate of first order derivatives in the L_pnorm. An overview of integral representations and their application to partial differential equations can be found in H. Begehr's and R. P.Gilbert's two volumes [2]. Interior esitmates in the Hijlder norm for very general (elliptic) systems of partial differential equations can be found in A. Douglis' and L. Nirenberg's paper [7], while estimates in the L_p-norm are contained, for instance, in the papers I ofthe threeauthors S. Agmon, A. Douglis and L. Nirenberg. In these papers [1,7] one can find further references.

Keywords:

• a priori estimates
• fundamental solutions
• kernel functions
• poisson kernel
• boundaryand domain integral representations
• monogenic and generalized monogenic functions
• cauchy kernel of clifford analysis

AMS:

• 35C15
• 35J15
• 31B10
• 30G20
• 30G35
• 35A10

¹The stay of U. Y¨ksel at Graz Technical University is supported by the Austrian Acadenlic Exchange Service

¹The stay of U. Y¨ksel at Graz Technical University is supported by the Austrian Acadenlic Exchange Service

Notes

¹The stay of U. Y¨ksel at Graz Technical University is supported by the Austrian Acadenlic Exchange Service