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math.AP2023
Quantified Legendreness and the regularity of minima
Cristiana De Filippis, Lukas Koch, Jan Kristensen
We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and -smoothness results for vector va…
math.AP2023★ 60 cited
Regularity for double phase problems at nearly linear growth
Cristiana De Filippis, Giuseppe Mingione
Minima of functionals of the type $$ w\mapsto \int_Ω\left[\snr{Dw}\log(1+\snr{Dw})+a(x)\snr{Dw}^{q}\right] \dx\,, \quad 0\leq a(\cdot) \in C^{0, α}\,,$$ with $Ω\subset \er^n$, have…