31 research outputs found
Elliptic problems with growth in nonreflexive Orlicz spaces and with measure or data
We investigate solutions to nonlinear elliptic Dirichlet problems of the type
where is a bounded Lipschitz domain in
and is a Carath\'eodory's function. The growth
of~the~monotone vector field with respect to the variables is
expressed through some -functions and . We do not require any
particular type of growth condition of such functions, so we deal with problems
in nonreflexive spaces. When the problem involves measure data and weakly
monotone operator, we prove existence. For -data problems with strongly
monotone operator we infer also uniqueness and regularity of~solutions and
their gradients in the scale of Orlicz-Marcinkiewicz spaces
Gradient Riesz potential estimates for a general class of measure data quasilinear systems
We study the gradient regularity of solutions to measure data elliptic
systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel
measure, pointwise estimates for the gradient of solutions are provided in
terms of the truncated Riesz potential. This allows us to show a precise
transfer of regularity from data to solutions on various scales.Comment: 36 page