PUB - Publikationen an der Universität Bielefeld

If (E,D) is a symmetric, regular, strongly local Dirichlet form on L2(X,m), admitting a carr & eacute; du champ operator Gamma, and p>1 is a real number, then one can define a nonlinear form Ep by the formula E-p(u,v)=integral(X)Gamma(u)(p-2)/(2)Gamma(u,v)dm, where u, v belong to an appropriate subspace of the domain D. We show that E-p is a nonlinear Dirichlet form in the sense introduced by P. van Beusekom. We then construct the associated Choquet capacity. As a particular case we obtain the nonlinear form associated with the p-Laplace operator on W-0(1,p). Using the above procedure, for each n-dimensional quasiregular mapping f we construct a nonlinear Dirichlet form E-n (p=n) such that the components of f become harmonic functions with respect to E-n. Finally, we obtain Caccioppoli type inequalities in the intrinsic metric induced by E, for harmonic functions with respect to the form E-p.