Uniform Bounds for Strongly Competing Systems: The Optimal Lipschitz Case
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| 008 | 210128e20151101xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0867-9 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0867-9 | ||
| 245 | 0 | 0 | |a Uniform Bounds for Strongly Competing Systems: The Optimal Lipschitz Case |h [Elektronische Daten] |c [Nicola Soave, Alessandro Zilio] |
| 520 | 3 | |a For a class of systems of semi-linear elliptic equations, including $$-\Delta u_i=f_i(x,u_i) - \beta u_i\sum_{j\neq i}a_{ij}u_j^p,\quad i=1,\dots,k,$$ - Δ u i = f i ( x , u i ) - β u i ∑ j ≠ i a i j u j p , i = 1 , ⋯ , k , for p=2 (variational-type interaction) or p = 1 (symmetric-type interaction), we prove that uniform $${L^\infty}$$ L ∞ boundedness of the solutions implies uniform boundedness of their Lipschitz norm as $${\beta \to +\infty}$$ β → + ∞ , that is, in the limit of strong competition. This extends known quasi-optimal regularity results and covers the optimal case for this class of problems. The proofs rest on monotonicity formulae of Alt-Caffarelli-Friedman and Almgren type in the variational setting, and on the Caffarelli-Jerison-Kenig almost monotonicity formula in the symmetric one. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Soave |D Nicola |u Mathematisches Institut, Justus Liebig Universität Giessen, Arndtstrasse 2, 35392, Giessen, Germany |4 aut | |
| 700 | 1 | |a Zilio |D Alessandro |u Centre d'analyse et de mathématique sociales, École des Hautes Études en Sciences Sociales, 190-198 Avenue de France, 75244, Paris Cedex 13, France |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 647-697 |x 0003-9527 |q 218:2<647 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0867-9 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0867-9 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Soave |D Nicola |u Mathematisches Institut, Justus Liebig Universität Giessen, Arndtstrasse 2, 35392, Giessen, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zilio |D Alessandro |u Centre d'analyse et de mathématique sociales, École des Hautes Études en Sciences Sociales, 190-198 Avenue de France, 75244, Paris Cedex 13, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 647-697 |x 0003-9527 |q 218:2<647 |1 2015 |2 218 |o 205 | ||