TalksBubbling along submanifolds for a non linear elliptic problem with neumann boundary conditions at higher critical exponents
108
reads
In this talk we consider the equation $-\Delta u +\lambda u- u^{\frac{n-k+2}{n-k-2}} =0\,\hbox{ in }\,\O \subset\,\R^{n}$, under zero Neumann boundary conditions, where $\O$ is open, smooth and bounded and where $\lambda$ is a positive and large real number. We prove existence of positive solutions concentrating along a submanifold $K$ of the boundary $\partial\O$ with dim $(K) = k$, as $\lambda\to\,+\infty$. This is a joint work with M. del Pino and F. Mahmoudi.
reads
Monica Musso
2011-08-22
15:00:00 - 15:50:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
In this talk we consider the equation $-\Delta u +\lambda u- u^{\frac{n-k+2}{n-k-2}} =0\,\hbox{ in }\,\O \subset\,\R^{n}$, under zero Neumann boundary conditions, where $\O$ is open, smooth and bounded and where $\lambda$ is a positive and large real number. We prove existence of positive solutions concentrating along a submanifold $K$ of the boundary $\partial\O$ with dim $(K) = k$, as $\lambda\to\,+\infty$. This is a joint work with M. del Pino and F. Mahmoudi.