For a competition-diffusion system involving the fractional Laplacian of the form
Mots clés : Fractional Laplacian, Spatial segregation, Strongly competing systems, Entire solutions
@article{AIHPC_2018__35_3_831_0, author = {Terracini, Susanna and Vita, Stefano}, title = {On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {831--858}, publisher = {Elsevier}, volume = {35}, number = {3}, year = {2018}, doi = {10.1016/j.anihpc.2017.08.004}, mrnumber = {3778654}, zbl = {1393.35042}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2017.08.004/} }
TY - JOUR AU - Terracini, Susanna AU - Vita, Stefano TI - On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition JO - Annales de l'I.H.P. Analyse non linéaire PY - 2018 SP - 831 EP - 858 VL - 35 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2017.08.004/ DO - 10.1016/j.anihpc.2017.08.004 LA - en ID - AIHPC_2018__35_3_831_0 ER -
%0 Journal Article %A Terracini, Susanna %A Vita, Stefano %T On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition %J Annales de l'I.H.P. Analyse non linéaire %D 2018 %P 831-858 %V 35 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2017.08.004/ %R 10.1016/j.anihpc.2017.08.004 %G en %F AIHPC_2018__35_3_831_0
Terracini, Susanna; Vita, Stefano. On the asymptotic growth of positive solutions to a nonlocal elliptic blow-up system involving strong competition. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 3, pp. 831-858. doi : 10.1016/j.anihpc.2017.08.004. http://www.numdam.org/articles/10.1016/j.anihpc.2017.08.004/
[1] On phase-separation model: asymptotics and qualitative properties, Arch. Ration. Mech. Anal., Volume 208 (2013), pp. 163–200 | DOI | MR | Zbl
[2] Existence and stability of entire solutions of an elliptic system modeling phase separation, Adv. Math., Volume 243 (2013), pp. 102–126
[3] An approach to symmetrization via polarization, Trans. Am. Math. Soc., Volume 352 (2000), pp. 1759–1796 | MR | Zbl
[4] Nonlinear equations for fractional Laplacians, I: regularity, maximum principles, and Hamiltonian estimates, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 31 (2014) no. 1 | DOI | Numdam | MR | Zbl
[5] An extension problem related to the fractional Laplacian, Commun. Partial Differ. Equ., Volume 32 (2007) no. 8, pp. 1245–1260 | DOI | MR | Zbl
[6] Semilinear elliptic problems with mixed Dirichlet–Neumann boundary conditions, J. Funct. Anal., Volume 199 (2003) no. 2, pp. 468–507 | DOI | MR | Zbl
[7] Some symmetry results for entire solutions of an elliptic system arising in phase separation, Discrete Contin. Dyn. Syst., Volume 34 (2014) no. 6, pp. 2505–2511 | DOI | MR | Zbl
[8] Monotonicity and 1-dimensional symmetry for solutions of an elliptic system arising in Bose–Einstein condensation, Arch. Ration. Mech. Anal., Volume 213 (2014) no. 1, pp. 287–326 | DOI | MR | Zbl
[9] Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition, Commun. Pure Appl. Math., Volume 63 (2010), pp. 267–302 | DOI | MR | Zbl
[10] Hardy-Type Inequalities, Pitman Research Notes in Mathematics Series, vol. 219, Longman Scientific & Technical, Harlow, 1990 | MR | Zbl
[11] Unique continuation for fractional Schrödinger equations with rough potential, 2013 (preprint) | arXiv | MR
[12] Partial symmetry and asymptotic behavior for some elliptic variational problems, Calc. Var. Partial Differ. Equ., Volume 18 (2003), pp. 57–75 | DOI | MR | Zbl
[13] Liouville theorems and 1-dimensional symmetry for solutions of an elliptic system modelling phase separation, Adv. Math., Volume 279 (2015), pp. 29–66 | DOI | MR | Zbl
[14] Entire solutions with exponential growth for an elliptic system modeling phase-separation, Nonlinearity, Volume 27 (2014) no. 2, pp. 305–342 | DOI | MR | Zbl
[15] Uniform bounds for strongly competing systems: the optimal Lipschitz case, Arch. Ration. Mech. Anal., Volume 218 (2015) no. 2, pp. 647–697 | DOI | MR | Zbl
[16] Multidimensional entire solutions for an elliptic system modelling phase separation, Anal. PDE, Volume 9 (2016) no. 5, pp. 1019–1041 | DOI | MR | Zbl
[17] On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 34 (2017) no. 3, pp. 625–654 | DOI | Numdam | MR | Zbl
[18] Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian, J. Eur. Math. Soc., Volume 18 (2016) no. 12, pp. 2865–2924 | DOI | MR | Zbl
[19] Uniform Hölder regularity with small exponent in competition-fractional diffusion systems, Discrete Contin. Dyn. Syst., Volume 34 (2014) no. 6, pp. 2669–2691 | DOI | MR | Zbl
[20] On the De Giorgi type conjecture for an elliptic system modeling phase separation, Commun. Partial Differ. Equ., Volume 39 (2014) no. 4, pp. 696–739 | MR | Zbl
[21] On the uniqueness of solutions of an nonlocal elliptic system, Math. Ann., Volume 365 (2016) no. 1, pp. 105–153 | MR
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