Calculus of Variations and Geometric Measure Theory

F. Farroni - L. Greco - G. Moscariello - G. Zecca

Noncoercive quasilinear elliptic operators with singular lower order terms

created by farroni on 29 Jun 2020
modified on 19 Apr 2021


Published Paper

Inserted: 29 jun 2020
Last Updated: 19 apr 2021

Journal: Calc. Var. and Partial Differential Equations
Year: 2021
Doi: 10.1007/s00526-021-01965-z
Links: Springer link to the paper


We consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in Marcinkiewicz spaces. We prove the existence of a solution to the corresponding Dirichlet problem. The associated obstacle problem is also solved. Finally, we show higher integrability of a solution to the Dirichlet problem when the datum is more regular.