First Order Equations

  • Bernard Dacorogna
  • Paolo Marcellini
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 37)


In this chapter we will deal with first order scalar partial differential equations. The problem under consideration is
$$ \left\{ {\begin{array}{*{20}{c}} {F(x,u(x),Du(x)) = 0,a.ein\Omega } \\ {u = \varphi ,on\partial \Omega ,} \end{array}} \right. $$
Where \( \Omega \subset {\mathbb{R}^n} \) is an open set, \( F:\Omega \times \mathbb{R} \times {\mathbb{R}^n} \to \mathbb{R} \)is continuous and \( \varphi \in {W^{1,\infty }}(\Omega ) \).


Convex Hull Compatibility Condition Convex Combination Boundary Data Lower Semicontinuity 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Bernard Dacorogna
    • 1
  • Paolo Marcellini
    • 2
  1. 1.Department of MathematicsEcole Polytechnic Fédérale de LausanneLausanneSwitzerland
  2. 2.Dipartimento di Matematica “U. Dini”Università di FirenzeFirenzeItaly

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