Milan Journal of Mathematics

, Volume 82, Issue 2, pp 407–422 | Cite as

Hodge-type Decomposition for Time-dependent First-order Parabolic Operators with Non-constant Coefficients: The Variable Exponent Case

  • R. S. Kraußhar
  • M. M. Rodrigues
  • N. VieiraEmail author


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.

Mathematics Subject Classification

Primary 30G35 Secondary: 35Q41 35A08 46E35 46E30 34L40 


Clifford analysis Witt basis parabolic-type Dirac operator timedependent operators Schrödinger equation fundamental solution variable exponent spaces regularization procedure Hodge decomposition 


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© Springer Basel 2014

Authors and Affiliations

  1. 1.Fachgebiet MathematikErziehungswissenschaftliche Fakultät Universität ErfurtErfurtGermany
  2. 2.CIDMA - Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal

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