Natural boundary value problems for weighted form laplacians

Kozłowski, Wojciech; Pierzchalski, Antoni

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 2, pp. 343-367.

The four natural boundary problems for the weighted form Laplacians $L=ad\delta +b\delta d,a,b>0$ acting on polynomial differential forms in the $n$-dimensional Euclidean ball are solved explicitly. Moreover, an algebraic algorithm for generating a solution from the boundary data is given in each case.

Classification : 35J67, 35J25, 34K10

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