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Linear Partial Differential Equations of Second Order

  • Marin Marin
  • Andreas Öchsner
Chapter

Abstract

Let us consider the differential operator
$$L(u)(x)\!=\!\sum _{i, j=1}^{n}a_{ij}(x)\frac{\partial ^{2} u}{\partial x_{i}\partial x_{j}}(x)\!+\! \sum _{j=1}^{n}a_{j}(x)\frac{\partial u}{\partial x_{j}}(x)\!+\!a_{0}(x)u(x),$$
in which the coefficients \(a_{ij}\;(i, j=\overline{1,n}),\; a_{j}\,(j=\overline{1,n})\) and \(a_{0}\) are regular functions which depend only on one variable x and which are defined on an open set \(\Omega \) from \(R^{n}\), where \(\Omega \) is not necessarily bounded.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTransilvania University of BrasovBrasovRomania
  2. 2.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingenGermany

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