Dirichlet-Type Problems for the Iterated Dirac Operator on the Unit Ball in Clifford Analysis
We study a class of Dirichlet-type problems for null solutions to iterated Dirac operators on the unit ball of R n with boundary data given by function in Open image in new window (1<p<+∞). Applying Almansi-type decomposition theorems for null solutions to iterated Dirac operators, our Dirichlet-type problems for null solutions to iterated Dirac operators is transferred to Dirichlet-type problems for monogenic functions or harmonic functions. By introducing shifted Euler operators and making use of Clifford-Cauchy transform, we get its unique solution and its integral representation.
This work was supported by FEDER funds through COMPETE—Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”), by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690 and by NNSF of China under Grant No. 60873249. The first author is the recipient of Postdoctoral Foundation from FCT (Portugal) under Grant No. SFRH/BPD/74581/2010 and from China under Grant No. 201003111.
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