caa a22 4500 46324804X CHVBK 20180405153331.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s10455-006-9049-1 doi (NATIONALLICENCE)springer-10.1007/s10455-006-9049-1 Bourgoin Jean-Christophe Laboratoire de Mathematiques et Physique Théorique, Université de Tours, Parc Grandmont, 37200, Tours, France aut On the minimality of the p -harmonic map $$x/\x\$$ for weighted energy [Elektronische Daten] [Jean-Christophe Bourgoin] In this paper, we study the minimality of the map $$\frac{x}{\|x\|}$$ for the weighted energy functional $$E_{f,p}= \int_{\mathbf{B}^n}f(r)\|\nabla u\|^p dx$$ , where $$f : [0,1] \rightarrow \mathbb{R}^{+}$$ is a continuous function. We prove that for any integer $$p \in \{2, \ldots, n-1\}$$ and any non-negative, non-decreasing continuous function f, the map $$\frac{x}{\|x\|}$$ minimizes E f,p among the maps in $$W^{1,p}(\mathbf{B}^n, \mathbb{S}^{n-1})$$ which coincide with $$\frac{x}{\|x\|}$$ on $$\partial \mathbf{B}^n$$ . The case p=1 has been already studied in [Bourgoin J.-C. Calc. Var. (to appear)]. Then, we extend results of Hong (see Ann. Inst. Poincaré Anal. Non-linéaire 17: 35-46 (2000)). Indeed, under the same assumptions for the function f, we prove that in dimension n ≥ 7 for any real $$p \in [2,n)$$ with $$p \in (n-2\sqrt{n-1},n)$$ , the map $$\frac{x}{\|x\|}$$ minimizes E f,p among the maps in $$W^{1,p}(\mathbf{B}^n, \mathbb{S}^{n-1})$$ which coincide with $$\frac{x}{\|x\|}$$ on $$\partial \mathbf{B}^n$$ . Springer Science + Business Media B.V., 2006 Minimizing map nationallicence p -Harmonic map nationallicence p -Energy nationallicence Weighted energy nationallicence Weakly p -harmonic map nationallicence Annals of Global Analysis and Geometry Kluwer Academic Publishers 32/1(2007-08-01), 1-13 0232-704X 32:1<1 2007 32 10455 https://doi.org/10.1007/s10455-006-9049-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10455-006-9049-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bourgoin Jean-Christophe Laboratoire de Mathematiques et Physique Théorique, Université de Tours, Parc Grandmont, 37200, Tours, France aut NATIONALLICENCE 773 0- Annals of Global Analysis and Geometry Kluwer Academic Publishers 32/1(2007-08-01), 1-13 0232-704X 32:1<1 2007 32 10455 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer