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On the hölder continuity of solutions of elliptic partial differential equations in two variables with coefficients in L∞

✍ Scribed by Kjell-Ove Widman

Publisher
John Wiley and Sons
Year
1969
Tongue
English
Weight
523 KB
Volume
22
Category
Article
ISSN
0010-3640

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## KJELL-OVE WIDMAN 51. We shall consider (weak) solutions of the equation in a bounded domain R c R", n 5 2. The equation is supposed to satisfy aaj E L , , A, IEi2 5 ai\*[Jj 5 AZ IEI2, a\*j = aji. If R satisfies an internal sphere condition, we can prove THEOREM 1 . Let u be a bounded solution o

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## Abstract We study the existence of solutions of the general elliptic system of partial differential equations in the space where the principal part may be represented with the help of a CLIFFORDalgebra 𝔄. We construct an integral representation and discuss the properties of the kernels.