Quantified Legendreness and the regularity of minima
<p>We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and 2<em>d</em>-smoothness results for vector valued minimizers of possibly degenerate functionals. Our framework covers convex, anisotropic...
| Những tác giả chính: | , , |
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| Định dạng: | Journal article |
| Ngôn ngữ: | English |
| Được phát hành: |
Springer
2024
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| Tóm tắt: | <p>We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and 2<em>d</em>-smoothness results for vector valued minimizers of possibly degenerate functionals. Our framework covers convex, anisotropic polynomials as prototypical model examples—in particular, we improve in an essentially optimal fashion Marcellini’s original results (Marcellini in Arch Rat Mech Anal 105:267–284, 1989).</p> |
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