Regularity of solutions to higher-order integrals of the calculus of variations
We obtain new regularity conditions for problems of calculus of variations with higher-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main regularity result asserts that autonomous integral functionals with a Lagrangian having coercive partial derivatives...
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| Format: | article |
| Language: | eng |
| Published: |
1000
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| Online Access: | http://hdl.handle.net/10773/4090 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/4090 |
| Summary: | We obtain new regularity conditions for problems of calculus of variations with higher-order derivatives. As a corollary, we get non-occurrence of the Lavrentiev phenomenon. Our main regularity result asserts that autonomous integral functionals with a Lagrangian having coercive partial derivatives with respect to the higher-order derivatives admit only minimisers with essentially bounded derivatives. |
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