Sharp capacity estimates for annuli in Rn and in metric spaces
2014 (English)Conference paper, Presentation (Refereed)
We obtain estimates for the nonlinear variational capacity of annuli in weighted Rn and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted Rn. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted Rn, which are based on quasiconformality of radial stretchings in Rn.
Place, publisher, year, edition, pages
2014. 1-42 p.
annulus, capacity, doubling measure, exponent sets, Jacobian, metric space, Newtonian space, p-admissible weight, Poincar´e inequality, quasiconformal mapping, radial stretching, radial weight, reverse-doubling, sharp estimate, Sobolev ca- pacity, Sobolev space, upper gradient, variational capacity, weighted Rn.Mathematics Subject Classification (2010): Primary: 31C45; Secondary: 30C65, 30L99
IdentifiersURN: urn:nbn:se:liu:diva-115872OAI: oai:DiVA.org:liu-115872DiVA: diva2:796909
School on Nonlinear Analysis, Function Spaces and Applications 10, Trest, Czech republic, 9-15 juni 2014