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The Existence of Weak Solutions to Non-homogeneous A-Dirac Equations with Dirichlet Boundary Data

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Abstract

This paper is concerned with the weak solutions to a class of non-homogeneous A-Dirac equations DA(x, u, Du) + B(x, u, Du) = 0 with the Dirichlet boundary data. By means of the Poincaré inequalities of the Clifford valued function and some assumptions on operators A and B, we obtain the existence and uniqueness of solution to the scalar part of \({{\int_{\Omega}}{\overline{A(x, u, Du)}}D{\varphi}\,dx + {\int_{\Omega}}{\overline{B(x, u, Du)}}{\varphi}\,dx = 0}\). for each \({\varphi \in W^{1,p}_0 (\Omega, C\ell_n^k)}\).

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Correspondence to Yueming Lu.

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This work was supported by the National Natural Science Foundation of China (No. 11071048).

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Lu, Y., Bao, G. The Existence of Weak Solutions to Non-homogeneous A-Dirac Equations with Dirichlet Boundary Data. Adv. Appl. Clifford Algebras 24, 151–162 (2014). https://doi.org/10.1007/s00006-013-0428-y

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  • DOI: https://doi.org/10.1007/s00006-013-0428-y

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