Intrinsically $$p$$ p -biharmonic maps

Autor: Peter Hornung, Roger Moser
Rok vydání: 2013
Předmět:
Zdroj: Hornung, P & Moser, R 2014, ' Intrinsically p-biharmonic maps ', Calculus of Variations and Partial Differential Equations, vol. 51, no. 3-4, pp. 597-620 . https://doi.org/10.1007/s00526-013-0688-3
ISSN: 1432-0835
0944-2669
DOI: 10.1007/s00526-013-0688-3
Popis: For a compact Riemannian manifold $$N$$ , a domain $$\Omega \subset \mathbb {R}^m$$ and for $$p\in (1, \infty )$$ , we introduce an intrinsic version $$E_p$$ of the $$p$$ -biharmonic energy functional for maps $$u : \Omega \rightarrow N$$ . This requires finding a definition for the intrinsic Hessian of maps $$u : \Omega \rightarrow N$$ whose first derivatives are merely $$p$$ -integrable. We prove, by means of the direct method, existence of minimizers of $$E_p$$ within the corresponding intrinsic Sobolev space, and we derive a monotonicity formula. Finally, we also consider more general functionals defined in terms of polyconvex functions.
Databáze: OpenAIRE
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