A general class of free boundary problems for fully nonlinear parabolic equations
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605496439 | ||
| 003 | CHVBK | ||
| 005 | 20210128105157.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150801xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10231-014-0413-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0413-7 | ||
| 245 | 0 | 2 | |a A general class of free boundary problems for fully nonlinear parabolic equations |h [Elektronische Daten] |c [Alessio Figalli, Henrik Shahgholian] |
| 520 | 3 | |a In this paper, we consider the fully nonlinear parabolic free boundary problem $$\begin{aligned} \left\{ \begin{array}{ll} F(D^2u) -\partial _{t} u=1 &{} \text {a.e. in }Q_1 \cap \Omega \\ |D^2 u| + |\partial _{t} u| \le K &{} \text {a.e. in }Q_1{\setminus }\Omega , \end{array} \right. \end{aligned}$$ F ( D 2 u ) - ∂ t u = 1 a.e. in Q 1 ∩ Ω | D 2 u | + | ∂ t u | ≤ K a.e. in Q 1 \ Ω , where $$K>0$$ K > 0 is a positive constant, and $$\Omega $$ Ω is an (unknown) open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that $$W_x^{2,n} \cap W_t^{1,n} $$ W x 2 , n ∩ W t 1 , n solutions are locally $$C_x^{1,1}\cap C_t^{0,1} $$ C x 1 , 1 ∩ C t 0 , 1 inside $$Q_1$$ Q 1 . A key starting point for this result is a new BMO-type estimate, which extends to the parabolic setting the main result inCaffarelli and Huang (Duke Math J 118(1):1-17, 2003). Once optimal regularity for $$u$$ u is obtained, we also show regularity for the free boundary $$\partial \Omega \cap Q_1$$ ∂ Ω ∩ Q 1 under the extra condition that $$\Omega \supset \{ u \ne 0 \}$$ Ω ⊃ { u ≠ 0 } , and a uniform thickness assumption on the coincidence set $$\{ u = 0 \}$$ { u = 0 } . | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Free boundaries |2 nationallicence | |
| 690 | 7 | |a Regularity |2 nationallicence | |
| 690 | 7 | |a Parabolic fully nonlinear |2 nationallicence | |
| 700 | 1 | |a Figalli |D Alessio |u Mathematics Department, The University of Texas at Austin, 78712-1202, Austin, TX, USA |4 aut | |
| 700 | 1 | |a Shahgholian |D Henrik |u Department of Mathematics, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 1123-1134 |x 0373-3114 |q 194:4<1123 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0413-7 |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/s10231-014-0413-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Figalli |D Alessio |u Mathematics Department, The University of Texas at Austin, 78712-1202, Austin, TX, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Shahgholian |D Henrik |u Department of Mathematics, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/4(2015-08-01), 1123-1134 |x 0373-3114 |q 194:4<1123 |1 2015 |2 194 |o 10231 | ||
| 986 | |a SWISSBIB |b 560493258 | ||