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


One of the main purposes of this book is to study the Dirichlet problem
$$ \left\{ {\begin{array}{*{20}{c}} {{F_i}\left( {x.u(x),Du(x)} \right) = 0,a.e.x \in \Omega ,i = 1, \ldots ,I} \\ {u(x) = \varphi (x),x \in \partial \Omega ,} \end{array}} \right. $$
Where \( \Omega \subset {\mathbb{R}^n} \) is an open set, \( u:\Omega \to {\mathbb{R}^m} \) and therefore \( Du \in {\mathbb{R}^{m \times n}} \) (if m = 1 we say that the problem is scalar and otherwise we say that it is vectorial), \( {F_i}:\Omega \times {\mathbb{R}^m} \times {\mathbb{R}^{m \times n}} \to \mathbb{R},{F_i} = {F_i}(x,s,\xi ),i = 1, \ldots ,I, \) are given. The boundary condition rp is prescribed (depending of the context it will be either continuously differentiable or only Lipschitz-continuous).


Viscosity Solution Compatibility Condition Boundary Data Scalar Case Eikonal Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations