Bonner mathematische Schriften, Issue 370Mathematisches Institut der Universität, 2005 - Mathematics |
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affine function barycenter bounded functions CALIFORNIA SAN DIEGO Cc(M classical Dirichlet form continuous map convergence d(zq define the nonlinear definition of nonlinear DIEGO OF CALIFORNIA DIEGO THE LIBRARIES discrete nonlinear Dirichlet discrete nonlinear energy Doc(E dox,e(y doze(y dy)m(dx dµ(x E D(E EN(u EN(v energy for maps equivariant map Euclidean domain finite tree form Ɛ Furthermore harmonic maps Hence Hölder continuous holds Hom(g Korevaar/Schoen L²(D L²(M Lemma LIBRARIES SAN DIEGO lim sup lim t-0 Lipschitz continuous map g maps with values Markov kernels measurable map measure space nonlinear Dirichlet problem nonlinear energy function NPC spaces number of edges p-equivariant measurable map problem for g projections proof of Theorem Proposition regular Dirichlet form resp Riemannian manifold semigroup of Markov sequel solution solve the nonlinear spider Subsection supp[v Theorem 2.7 triangles triangulation Th UNIV universal cover v₁ VN g yields Σ Σ ΣΣ