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Everywhere regularity for a class of elliptic systems with p, q growth conditions
Migliorini, Anna Paola
1999
Abstract
We shall prove everywhere regularity for weak solutions of elliptic
systems of the form
\[
\sum\frac{\partial}{\partial x_{i}}a\left(x,\mid Du\mid\right)u_{x_{i}}^{\alpha}=0
\]
under general p, q growth conditions and in particular for minimizers
of a class of variational integrals, both degenerate and non degenerate
ones, whose models are
\[
\begin{array}{c}
I_{1}\left(u\right)\quad=\quad\int_{\Omega}a\left(x\right)\mid Du\mid^{b\left(x\right)}dx,\\
I_{2}\left(u\right)\quad=\quad\int_{\Omega}a\left(x\right)\left(1+\mid Du\mid^{2}\right)^{\frac{b\left(x\right)}{2}}dx.
\end{array}
\]
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (1999)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Anna Paolo Migliorini, "Everywhere regularity for a class of elliptic systems with p, q growth conditions", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (1999), pp. 203-234.
Languages
en
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