Abstract
AbstractWe will establish an $$\varepsilon $$
ε
-regularity result for weak solutions to Legendre–Hadamard elliptic systems, under the a-priori assumption that the gradient $$\nabla u$$
∇
u
is small in $$\textrm{BMO}.$$
BMO
.
Focusing on the case of Euler–Lagrange systems to simplify the exposition, regularity results will be obtained up to the boundary, and global consequences will be explored. Extensions to general quasilinear elliptic systems and higher-order integrands is also discussed.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference51 articles.
1. Acerbi, E., Fusco, N.: A regularity theorem for minimizers of quasiconvex integrals. Arch. Ration. Mech. Anal. 99(3), 261–281 (1987). ISSN: 0003-9527. https://doi.org/10.1007/BF00284509
2. Adams, R.A., Fournier, J.: Sobolev Spaces. Academic Press (2003). ISBN 978-0-08-054129-7
3. Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. Commun. Pure Appl. Math. 17(1), 35–92 (1964). ISSN 00103640. https://doi.org/10.1002/cpa.3160170104
4. Boman, J.: $$L^p$$-estimates for very strongly elliptic systems, Department of Mathematics, University of Stockholm. Tech. Rep, Sweden (1982)
5. Campanato, S.: Alcune osservazioni relative alle soluzioni di equazioni ellittiche di ordine $$2m$$. Atti del Convegno sulle Equazioni alle Deriv. Parziali, pp.17–25 (1967)