6533b820fe1ef96bd127a3f3
RESEARCH PRODUCT
Sharp capacity estimates for annuli in weighted R^n and in metric spaces
Anders BjörnJana BjörnJuha Lehrbäcksubject
31C45 (Primary) 30C65 30L99 31B15 31C15 31E0 (Secondary)annulusmetric spacequasiconformal mappingMathematical Analysisexponent setsp-admissible weightSobolev spaceradial weightMathematics - Analysis of PDEsAnnulus; Doubling measure; Exponent sets; Metric space; Newtonian space; p-admissible weight; Poincare inequality; Quasiconformal mapping; Radial weight; Sobolev space; Variational capacityMatematisk analysPoincaré inequalitydoubling measureFOS: MathematicsNewtonian spacevariational capacityAnalysis of PDEs (math.AP)description
We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n 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 R^n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R^n, which are based on quasiconformality of radial stretchings in R^n.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-01-01 |