On the Dirichlet and Serrin Problems for the Inhomogeneous Infinity Laplacian in Convex Domains: Regularity and Geometric Results
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| 024 | 7 | 0 | |a 10.1007/s00205-015-0888-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0888-4 | ||
| 245 | 0 | 0 | |a On the Dirichlet and Serrin Problems for the Inhomogeneous Infinity Laplacian in Convex Domains: Regularity and Geometric Results |h [Elektronische Daten] |c [Graziano Crasta, Ilaria Fragalà] |
| 520 | 3 | |a Given an open bounded subset Ω of $${\mathbb{R}^n}$$ R n , which is convex and satisfies an interior sphere condition, we consider the pde $${-\Delta_{\infty} u = 1}$$ - Δ ∞ u = 1 in Ω, subject to the homogeneous boundary condition u = 0 on ∂Ω. We prove that the unique solution to this Dirichlet problem is power-concave (precisely, 3/4 concave) and it is of class C 1(Ω). We then investigate the overdetermined Serrin-type problem, formerly considered in Buttazzo and Kawohl (Int Math Res Not, pp 237-247, 2011), obtained by adding the extra boundary condition $${|\nabla u| = a}$$ | ∇ u | = a on ∂Ω; by using a suitable P-function we prove that, if Ω satisfies the same assumptions as above and in addition contains a ball which touches ∂Ω at two diametral points, then the existence of a solution to this Serrin-type problem implies that necessarily the cut locus and the high ridge of Ω coincide. In turn, in dimension n=2, this entails that Ω must be a stadium-like domain, and in particular it must be a ball in case its boundary is of class C 2. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Crasta |D Graziano |u Dipartimento di Matematica "G. Castelnuovo”, Univ. di Roma I, P.le A. Moro 2, 00185, Rome, Italy |4 aut | |
| 700 | 1 | |a Fragalà |D Ilaria |u Dipartimento di Matematica, Politecnico, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/3(2015-12-01), 1577-1607 |x 0003-9527 |q 218:3<1577 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0888-4 |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/s00205-015-0888-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Crasta |D Graziano |u Dipartimento di Matematica "G. Castelnuovo”, Univ. di Roma I, P.le A. Moro 2, 00185, Rome, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Fragalà |D Ilaria |u Dipartimento di Matematica, Politecnico, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/3(2015-12-01), 1577-1607 |x 0003-9527 |q 218:3<1577 |1 2015 |2 218 |o 205 | ||