A non-doubling Trudinger inequality
We establish a Trudinger inequality for functions that satisfy a suitable Poincarè inequality in a Euclidean space equipped with a Borel measure that need not be doubling.
We establish a Trudinger inequality for functions that satisfy a suitable Poincarè inequality in a Euclidean space equipped with a Borel measure that need not be doubling.
2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and which include as a particular case, the result of [3].
The - regularity of the gradient of weak solutions to nonlinear elliptic systems is proved.
The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.
Introduction. For bounded domains in satisfying the cone condition there are many embedding and module structure theorem for Sobolev spaces which are of great importance in solving partial differential equations. Unfortunately, most of them are wrong on arbitrary unbounded domains or on open manifolds. On the other hand, just these theorems play a decisive role in foundations of nonlinear analysis on open manifolds and in solving partial differential equations. This was pointed out by the author...