Multivalued problem with Robin boundary condition involving diffuse measure data and variable exponent

---

Résumé

We study a nonlinear elliptic problem with Robin type boundary condition, governed by a general Leray–Lions operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero 𝑝( ⋅ )-capacity. We prove an existence and uniqueness result of a weak solution.

Mots-clés

Robin boundary condition, diffuse measure, Biting Lemma of Chacon, maximal monotone graph, Radon measure data, weak solution, entropic solution, Leray–Lions operator, subdifferential operator