caa a22 4500 445843578 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00526-010-0332-4 doi (NATIONALLICENCE)springer-10.1007/s00526-010-0332-4 Bump solutions for the mesoscopic Allen-Cahn equation in periodic media [Elektronische Daten] [Matteo Novaga, Enrico Valdinoci] Given a double-well potential F, a $${\mathbb{Z}^n}$$-periodic function H, small and with zero average, and ε>0, we find a large R, a small δ and a function H ε which is ε-close to H for which the following two problems have solutions: 1.Find a set E ε,R whose boundary is uniformly close to ∂ B R and has mean curvature equal to −H ε at any point,2.Find u = u ε,R,δ solving $$ -\delta\,\Delta u + \frac{F'(u)}{\delta} +\frac{c_0}{2} H_\varepsilon = 0, $$such that u ε,R,δ goes from a δ-neighborhood of +1 in B R to a δ-neighborhood of −1 outside B R. Springer-Verlag, 2010 Novaga Matteo Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste, 63, 35121, Padova, Italy aut Valdinoci Enrico Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133, Rome, Italy aut Calculus of Variations and Partial Differential Equations Springer-Verlag 40/1-2(2011-01-01), 37-49 0944-2669 40:1-2<37 2011 40 526 https://doi.org/10.1007/s00526-010-0332-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0332-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Novaga Matteo Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste, 63, 35121, Padova, Italy aut NATIONALLICENCE 700 1- Valdinoci Enrico Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133, Rome, Italy aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 40/1-2(2011-01-01), 37-49 0944-2669 40:1-2<37 2011 40 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer