Higher differentiability of minimizers of convex variational integrals

By Menita Carozza, Jan Kristensen, Antonia Passarelli di Napoli. 2011

119 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/98906f22a9573c8c13183d601d37f36e7e6aee9a

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In Applied Mathematics

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Citations in the corpus

Non-autonomous functionals, borderline cases and related function classes (2016, background): “They have been the object of an intensive investigation during the last years, see for instance [8, 9, 11, 12, 13, 34, 43, 44, 54, 55].”
Parabolic equations with p, q-growth (2013, unknown): “[3,5,6,11,14,18,22,23] and the references therein.”
On the Regularity of Minima of Non-autonomous Functionals (2019, methodology): “Ω F (Dw) dx the interaction between boundedness of minima and dimensionless bounds has been considered in [13, 15, 30].”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “12) has also been considered in [48], in the vectorial case, where W 1,q-local regularity of minima has been obtained.”
Regularity results for vectorial minimizers of a class of degenerate convex integrals (2018, background): “1) through the following Gagliardo-Nirenberg type interpolation inequality, see also [5].”
Harnack inequalities for double phase functionals (2015, background): “Now, while in the case of an autonomous energy density of the type F (x,w,Dw) ≡ F (Dw) the regularity theory of minima of functionals with (p, q)-growth conditions is by now well-understood (see for instance [4, 5, 27, 13, 24, 29]), the case of non-autonomous integrals is still very much open and in”
Regularity for Double Phase Variational Problems (2015, background): “The previous theorem - involving the Nikolski spaceN - sharply extends previously known differentiability and integrability theorems valid in the p-Laplacean case [8], [24], [40], [41].”
Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems (2017, unknown): “This includes the classics [17,27,28,33,37,38,43,44,58,60–62], and the newer advances [11,13,13,14,22,31,41].”
Regularity of minimizers of autonomous convex variational integrals (2013, methodology): “Here w give a version suitable for our needs, partly for the sake of completeness and partly because the pr es nt set–up differs slightly from that of [3].”
Higher differentiability of minimizers of variational integrals with Sobolev coefficients (2012, unknown): “Before proceeding with the proof, we need to carry out an approximation procedure, which is essentially based on the arguments contained in [8].”