Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems
Local boundedness of minimizers of anisotropic functionals
Optimal Orlicz-Sobolev embeddings.
Optimal integrability of the Jacobian of orientation preserving maps
Dato un qualsiasi spazio invariante per riordinamenti su un insieme aperto , si determina il più piccolo spazio invariante per riordinamenti con la proprietà che se è una applicazione che mantiene l'orientamento e , allora appartiene localmente a .
Eigenfunctions of the Laplace-Beltrami Operator, and Isoperimetric and Isocapacitary Inequalities
Hardy inequalities with non-standard remainder terms
An optimal endpoint trace embedding
We find an optimal Sobolev-type space on all of whose functions admit a trace on subspaces of of given dimension. A corresponding trace embedding theorem with sharp range is established.
A sharp iteration principle for higher-order Sobolev embeddings
We survey results from the paper [CPS] in which we developed a new sharp iteration method and applied it to show that the optimal Sobolev embeddings of any order can be derived from isoperimetric inequalities. We prove thereby that the well-known link between first-order Sobolev embeddings and isoperimetric inequalities translates to embeddings of any order, a fact that had not been known before. We show a general reduction principle that reduces Sobolev type inequalities of any order involving...
Gradient regularity via rearrangements for -Laplacian type elliptic boundary value problems
A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.
Some results in the theory of Orlicz spaces and applications to variational problems
The sharp Sobolev inequality in quantitative form
Borderline sharp estimates for solutions to Neumann problems.
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