We report on some higher differentiability theorems valid for minimizers of integral functionals \(\int_{\Omega} f(D u) d x\), with non standard growth conditions of \((p, q)\) type. The main feature of our results is that the only regularity assumption made on \(f\) is a suitable form of uniform co
Differentiability for Bounded Minimizers of Some Anisotropic Integrals
β Scribed by A. Canale; A. D'Ottavio; F. Leonetti; M. Longobardi
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 91 KB
- Volume
- 253
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
We prove the existence of second weak derivatives for bounded minimizers u:
This allows us to improve on the Hausdorff dimension of the singular set of u.
π SIMILAR VOLUMES
## Existence of AC minimizers under the general hypotheses of lower semicontinuity, boundedness below, and superlinear growth at inΓΏnity in x (β’). Any nonconvex function h : R β [0; + β] will do, provided it is convex at = 0. Moreover, minimizers are shown to satisfy several regularity properties
The method of asymptotic integration of linear differential equations of the form introduced in [14] (see also [15], [l6]) is limited by two restrictions: