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Part of the book series: Birkhäuser Advanced Texts / Basler Lehrbücher ((BAT))


In this chapter we would like to consider in more details the Dirichlet problem for the p-Laplace operator, namely, if Ωis an open subset of ℝn, 1 < p < +∞ the problem

$$ \left\{ \begin{gathered} - \partial _{x_i } \left( {\left| {\nabla u} \right|^{p - 2} \partial _{x_i } u} \right) = f in \Omega , \hfill \\ u = 0 on \partial \Omega . \hfill \\ \end{gathered} \right. $$

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© 2009 Birkhäuser Verlag AG

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(2009). The p-Laplace Equation. In: Elliptic Equations: An Introductory Course. Birkhäuser Advanced Texts / Basler Lehrbücher. Birkhäuser Basel.

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