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Large $s$-harmonic functions and boundary blow-up solutions for the fractional Laplacian
Harmonic functions in union of chambers
1. | Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi, 55 - 20125 Milano, Italy |
2. | Dipartimento di Matematica "Giuseppe Peano", Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino |
References:
[1] |
L. Abatangelo, V. Felli and S. Terracini, On the sharp effect of attaching a thin handle on the spectral rate of convergence,, Journal of Functional Analysis, 266 (2014), 3632.
doi: 10.1016/j.jfa.2013.11.019. |
[2] |
L. Abatangelo, V. Felli and S. Terracini, Singularity of eigenfunctions at the junction of shrinking tubes. Part II,, Journal of Differential Equations, 256 (2014), 3301.
doi: 10.1016/j.jde.2014.02.010. |
[3] |
R. A. Adams and J. J. F. Fournier, Sobolev Spaces,, Academic Press 2003., (2003).
|
[4] |
G. Buttazzo and F. Santambrogio, Asymptotical compliance optimization for connected networks,, Netw. Heterog. Media, 2 (2007), 761.
doi: 10.3934/nhm.2007.2.761. |
[5] |
G. Buttazzo, F. Santambrogio and N. Varchon, Asymptotics of an optimal compliance-location problem,, ESAIM Control Optim. Calc. Var., 12 (2006), 752.
doi: 10.1051/cocv:2006020. |
[6] |
B. E. J. Dahlberg, Estimates for harmonic measure,, Arch. Rational Mech. Anal., 65 (1977), 275.
doi: 10.1007/BF00280445. |
[7] |
V. Felli and S. Terracini, Singularity of eigenfunctions at the junction of shrinking tubes. Part I,, J. Differential Equations, 255 (2013), 633.
doi: 10.1016/j.jde.2013.04.017. |
[8] |
T. Gilbarg, Elliptic Partial Differential Equations,, Springer, (2001). Google Scholar |
[9] |
V. Isakov, Inverse problems for Partial Differential Equations,, Springer, (2006).
|
[10] |
D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in nontangentially accessible domains,, Adv. in Math., 46 (1982), 80.
doi: 10.1016/0001-8708(82)90055-X. |
[11] |
T. Kato, Perturbation Theory for Linear Operators,, Springer-Verlag, (1995).
|
[12] |
A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems,, Springer, (1996).
doi: 10.1007/978-1-4612-5338-9. |
[13] |
M. Murata, On construction of Martin boundaries for second order elliptic equations,, Publ. Res. Inst. Math. Sci., 26 (1990), 585.
doi: 10.2977/prims/1195170848. |
[14] |
Y. Pinchover, On positive solutions of second-order elliptic equations, stability results, and classification,, Duke Math. J., 57 (1988), 955.
doi: 10.1215/S0012-7094-88-05743-2. |
[15] |
Y. Pinchover, On positive solutions of elliptic equations with periodic coefficients in unbounded domains,, in Maximum Principles and Eigenvalue Problems in Partial Differential Equations (Knoxville, (1987), 218.
|
[16] |
Y. Pinchover, On positive Liouville theorems and asymptotic behavior of solutions of Fuchsian type elliptic operators,, Ann. Inst.H. Poincaré Anal. Non Linéaire, 11 (1994), 313.
|
[17] |
R. G. Pinsky, Positive Harmonic Functions and Diffusion,, Cambridge Studies in Advanced Mathematics, (1995).
doi: 10.1017/CBO9780511526244. |
[18] |
M. Protter and H. Weinberger, Maximum Principles in Differential Equations,, Springer, (1984).
doi: 10.1007/978-1-4612-5282-5. |
[19] |
W. Rudin, Real and Complex Analysis,, McGraw-Hill, (1987).
|
show all references
References:
[1] |
L. Abatangelo, V. Felli and S. Terracini, On the sharp effect of attaching a thin handle on the spectral rate of convergence,, Journal of Functional Analysis, 266 (2014), 3632.
doi: 10.1016/j.jfa.2013.11.019. |
[2] |
L. Abatangelo, V. Felli and S. Terracini, Singularity of eigenfunctions at the junction of shrinking tubes. Part II,, Journal of Differential Equations, 256 (2014), 3301.
doi: 10.1016/j.jde.2014.02.010. |
[3] |
R. A. Adams and J. J. F. Fournier, Sobolev Spaces,, Academic Press 2003., (2003).
|
[4] |
G. Buttazzo and F. Santambrogio, Asymptotical compliance optimization for connected networks,, Netw. Heterog. Media, 2 (2007), 761.
doi: 10.3934/nhm.2007.2.761. |
[5] |
G. Buttazzo, F. Santambrogio and N. Varchon, Asymptotics of an optimal compliance-location problem,, ESAIM Control Optim. Calc. Var., 12 (2006), 752.
doi: 10.1051/cocv:2006020. |
[6] |
B. E. J. Dahlberg, Estimates for harmonic measure,, Arch. Rational Mech. Anal., 65 (1977), 275.
doi: 10.1007/BF00280445. |
[7] |
V. Felli and S. Terracini, Singularity of eigenfunctions at the junction of shrinking tubes. Part I,, J. Differential Equations, 255 (2013), 633.
doi: 10.1016/j.jde.2013.04.017. |
[8] |
T. Gilbarg, Elliptic Partial Differential Equations,, Springer, (2001). Google Scholar |
[9] |
V. Isakov, Inverse problems for Partial Differential Equations,, Springer, (2006).
|
[10] |
D. S. Jerison and C. E. Kenig, Boundary behavior of harmonic functions in nontangentially accessible domains,, Adv. in Math., 46 (1982), 80.
doi: 10.1016/0001-8708(82)90055-X. |
[11] |
T. Kato, Perturbation Theory for Linear Operators,, Springer-Verlag, (1995).
|
[12] |
A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems,, Springer, (1996).
doi: 10.1007/978-1-4612-5338-9. |
[13] |
M. Murata, On construction of Martin boundaries for second order elliptic equations,, Publ. Res. Inst. Math. Sci., 26 (1990), 585.
doi: 10.2977/prims/1195170848. |
[14] |
Y. Pinchover, On positive solutions of second-order elliptic equations, stability results, and classification,, Duke Math. J., 57 (1988), 955.
doi: 10.1215/S0012-7094-88-05743-2. |
[15] |
Y. Pinchover, On positive solutions of elliptic equations with periodic coefficients in unbounded domains,, in Maximum Principles and Eigenvalue Problems in Partial Differential Equations (Knoxville, (1987), 218.
|
[16] |
Y. Pinchover, On positive Liouville theorems and asymptotic behavior of solutions of Fuchsian type elliptic operators,, Ann. Inst.H. Poincaré Anal. Non Linéaire, 11 (1994), 313.
|
[17] |
R. G. Pinsky, Positive Harmonic Functions and Diffusion,, Cambridge Studies in Advanced Mathematics, (1995).
doi: 10.1017/CBO9780511526244. |
[18] |
M. Protter and H. Weinberger, Maximum Principles in Differential Equations,, Springer, (1984).
doi: 10.1007/978-1-4612-5282-5. |
[19] |
W. Rudin, Real and Complex Analysis,, McGraw-Hill, (1987).
|
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