Optimal Regularity for Nonlinear Elliptic Equations with Right-hand Side Measure in Variable Exponent Spaces

The Calderón-zygmund Theory for Elliptic Problems with Measure Data

We consider non-linear elliptic equations having a measure in the right hand side, of the type div a(x,Du) = μ, and prove differentiability and integrability results for solutions. New estimates in Marcinkiewicz spaces are also given, and the impact of the measure datum density properties on the regularity of solutions is analyzed in order to build a suitable Calderón-Zygmund theory for the pro...

Global and local estimates for nonlinear noncoercive elliptic equations with measure data

We study nonlinear noncoercive elliptic problems with measure data, proving first that the global estimates already known when the problem is coercive are still true for noncoercive problems. We then prove new estimates, on sets far from the support of the singular part of the right-hand side, in the energy space associated to the operator, which entails additional regularity results on the sol...

Uniqueness and Maximal Regularity for Nonlinear Elliptic Systems of N-laplace Type with Measure Valued Right Hand Side

Optimal Control of Semilinear Elliptic Equations in Measure Spaces

Optimal control problems in measure spaces governed by semilinear elliptic equations are considered. First order optimality conditions are derived and structural properties of their solutions, in particular sparsity, are discussed. Necessary and sufficient second order optimality conditions are obtained as well. On the basis of the sufficient conditions, stability of the solutions is analyzed. ...

Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces ∗

We prove optimal integrability results for solutions of the p(·)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L to variable exponent weak Lebesgue spaces.