Geodesic
Compact subdifferentials in Banach spaces and their applications to variational functionals
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 49 (2013), pp. 99-131

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We develop a theory of sublinear operators with compact values. Then, based on this theory, we construct a theory of first-order compact subdifferentials for maps in Banach spaces. The results are applicable to the calculation of compact subdifferentials of variational functionals with nonsmooth Lagrangians. 
@article{CMFD_2013_49_a2,
     author = {I. V. Orlov and Z. I. Khalilova},
     title = {Compact subdifferentials in {Banach} spaces and their applications to variational functionals},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {99--131},
     publisher = {mathdoc},
     volume = {49},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2013_49_a2/}
}
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I. V. Orlov; Z. I. Khalilova. Compact subdifferentials in Banach spaces and their applications to variational functionals. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 49 (2013), pp. 99-131. http://geodesic.mathdoc.fr/item/CMFD_2013_49_a2/