Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2604.07538 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918435755130880 |
|---|---|
| author | Irving, Christopher Li, Zhuolin Raiţă, Bogdan |
| author_facet | Irving, Christopher Li, Zhuolin Raiţă, Bogdan |
| contents | We prove that minimizers of variational integrals $$ \mathcal E(v)=\int_Ωf(v)\quad\text{for }v\in\mathcal M(Ω)\text{ such that } \mathscr{A} v=0, $$
are partially continuous provided that the integrands $f$ are strongly $\mathscr{A}$-quasiconvex in a suitable sense. We consider linear growth problems, linear PDE operators $\mathscr{A}$ of constant rank, and variations of the form $v+φ$ with $\mathscr{A}$-free $φ\in \mathrm{C}_{\mathrm{c}}^\infty(Ω)$. Our analysis also covers the ``potentials case'' $$ \mathcal F(u)=\int_Ωf( \mathscr{B} u)\quad\text{for } u\in\mathscr D'(Ω)\text{ such that }\mathscr B u\in \mathcal M(Ω), $$ where $\mathscr{B}$ is a different linear pde operator of constant rank. Both our main results extend to $x$-dependent integrands. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07538 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partial regularity for $\mathscr{A}$-quasiconvex variational problems of linear growth Irving, Christopher Li, Zhuolin Raiţă, Bogdan Analysis of PDEs 49N60, 35B65, 49J45, 28B05, 35E20 We prove that minimizers of variational integrals $$ \mathcal E(v)=\int_Ωf(v)\quad\text{for }v\in\mathcal M(Ω)\text{ such that } \mathscr{A} v=0, $$ are partially continuous provided that the integrands $f$ are strongly $\mathscr{A}$-quasiconvex in a suitable sense. We consider linear growth problems, linear PDE operators $\mathscr{A}$ of constant rank, and variations of the form $v+φ$ with $\mathscr{A}$-free $φ\in \mathrm{C}_{\mathrm{c}}^\infty(Ω)$. Our analysis also covers the ``potentials case'' $$ \mathcal F(u)=\int_Ωf( \mathscr{B} u)\quad\text{for } u\in\mathscr D'(Ω)\text{ such that }\mathscr B u\in \mathcal M(Ω), $$ where $\mathscr{B}$ is a different linear pde operator of constant rank. Both our main results extend to $x$-dependent integrands. |
| title | Partial regularity for $\mathscr{A}$-quasiconvex variational problems of linear growth |
| topic | Analysis of PDEs 49N60, 35B65, 49J45, 28B05, 35E20 |
| url | https://arxiv.org/abs/2604.07538 |