Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Borderline regularity in singular free boundary problems. |
| Συγγραφείς: |
Araújo, Damião J.1 (AUTHOR), Sobral, Aelson2 (AUTHOR), Teixeira, Eduardo V.3 (AUTHOR) eduardo.teixeira@okstate.edu, Urbano, José Miguel4,5 (AUTHOR) |
| Πηγή: |
Communications in Partial Differential Equations. 2026, Vol. 51 Issue 6, p619-636. 18p. |
| Θεματικοί όροι: |
*Calculus of variations, *Lipschitz continuity, *Smoothness of functions, *Boundary value problems |
| Περίληψη: |
In this article, we investigate the borderline regularity of local minimizers of energy functionals of the form ∫ 1 2 | Du | 2 + σ (u) , under minimal assumptions on the potential term σ . When σ is merely bounded and measurable, we show that sign-changing minimizers are Log-Lipschitz continuous, which represents the optimal regularity in this general setting. In the one-phase case, however, we establish gradient bounds for minimizers along their free boundaries, revealing a structural gain in regularity. Most notably, we prove that if σ is continuous, then minimizers are of class C 1 along the free boundary, thereby identifying a sharp threshold for differentiability in terms of the regularity of the potential. [ABSTRACT FROM AUTHOR] |
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