We establish higher differentiability results of integer order for solutions to a class of obstacle problems with nearly linear growth, provided that we assume a suitable extra integer differentiability property of Sobolev order on the gradient of the obstacle. Our results cover a large class of models for which the Lavrentiev phenomenon does not appear.
Cite this article
Chiara Gavioli, Higher differentiability for a class of obstacle problems with nearly linear growth conditions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 4, pp. 767–789DOI 10.4171/RLM/914