Abstract
In this paper we present a Hodge-type decomposition for variable exponent spaces. More concretely, we address some time-dependent parabolic firstorder partial differential operators with non-constant coefficients, where one of the components is the kernel of the parabolic-type Dirac operator. This decomposition is presented over different types of domains in the n-dimensional Euclidean space n-dimensional Euclidean space \({\mathbb{R}^{n}}\). The case of the time-dependent Schrödinger operator is included as a special case within this context.
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Kraußhar, R.S., Rodrigues, M.M. & Vieira, N. Hodge-type Decomposition for Time-dependent First-order Parabolic Operators with Non-constant Coefficients: The Variable Exponent Case. Milan J. Math. 82, 407–422 (2014). https://doi.org/10.1007/s00032-014-0228-4
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DOI: https://doi.org/10.1007/s00032-014-0228-4