Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact CNA Seminar Paolo Marcellini Universita' di Firenze Title: Nonlinear elliptic systems with general growth Abstract: We give some recent existence and interior regularity results for elliptic partial differential equations in divergence form of the type \begin{equation*} \sum_{i=1}^{n}\frac{\partial }{\partial x_{i}}a^{i}\left( x,u\left( x\right) ,Du\left( x\right) \right) =b\left( x,u\left( x\right) ,Du\left( x\right) \right) \,, \end{equation*}for $x\in \Omega$, open set of $\mathbb{R}^{n}$, $n\geq 2$, related to a vector field $a^{i}\left( x,s,\xi \right)$ locally Lipschitz continuous in $% \Omega \times \mathbb{R}\times \mathbb{R}^{n}$.More generally we consider elliptic systems of $m$ partial differential equations in divergence form of the type \begin{equation*} \sum_{i=1}^{n}\frac{\partial }{\partial x_{i}}a_{\alpha }^{i}\left( x,u\left( x\right) ,Du\left( x\right) \right) =b_{\alpha }\left( x,u\left( x\right) ,Du\left( x\right) \right) ,\;\;\;\;\alpha =1,2,\ldots ,m\,, \end{equation*}% for maps $u:\Omega \subset \mathbb{R}^{n}\rightarrow \mathbb{R}^{m}$. Here the vector field $\left( a_{\alpha }^{i}\left( x,s,\xi \right) \right)$ assumes values in the set of $m\times n$ matrices and it satisfies some \emph{general growth conditions} with respect to the gradient variable $\xi \in \mathbb{R}^{m\times n}$. Recording (avi): http://mm.math.cmu.edu/recordings/cna/CNA-PaoloMarcellini-Sep-18-2012.aviRecording (mp4): http://mm.math.cmu.edu/recordings/cna/CNA-PaoloMarcellini-Sep-18-2012.mp4Pdf File: Marcellini_Paolo.pdfDate: Tuesday, September 18, 2012Time: 1:30 pmLocation: Wean Hall 7218Submitted by:  David Kinderlehrer