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.
A nonlinear boundary problem involving the -bi-Laplacian operator.
A note on a two-weighted Sobolev inequality
A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev Space
A note on convergence of level sets.
A Note on Div-Curl Lemma
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].
A note on fractional integration
A note on Gehring's lemma.
A note on integral inequalities and embeddings of Besov spaces.
A note on regularity for nonlinear elliptic systems
The - regularity of the gradient of weak solutions to nonlinear elliptic systems is proved.
A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight
A note on the Poincaré inequality
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.
A note on wavelet bases in function spaces
A one-dimensional nonlinear degenerate elliptic equation.
A priori estimate for a system of differential operators.
A priori estimates in geometry and Sobolev spaces on open manifolds
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...
A property of multiplication in Sobolev spaces. Some applications
-condition for two weight functions and compact imbeddings of weighted Sobolev spaces
A remark on imbedding theorems for Sobolev weight spaces: The case of a domain with hölderian boundary.
A remark on the solvability of the Dirichlet problem in Sobolev spaces with power-type weights