-
Previous Article
A BKM's criterion of smooth solution to the incompressible viscoelastic flow
- CPAA Home
- This Issue
-
Next Article
A strongly singular parabolic problem on an unbounded domain
Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $R^n$
1. | Dipartimento di Matematica, Università di Torino, via Carlo Alberto, 10-10123 Torino, Italy |
References:
[1] |
Adimurthi, M. Grossi and S. Santra, Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem,, J. Funct. Anal., 240 (2006), 36.
doi: 10.1016/j.jfa.2006.07.011. |
[2] |
Adimurthi and S. Santra, Generalized Hardy-Rellich inequalities in critical dimensions and its applications,, Commun. Contemp. Math., 11 (2009), 367.
doi: 10.1142/S0219199709003405. |
[3] |
C. O. Alves and J. M. do Ò, Positive solutions of a fourth-order semilinear problem involving critical growth,, Adv. Nonlinear Stud., 2 (2002), 437.
|
[4] |
M. Bhakta and R. Musina, Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials,, Nonlinear Anal. T.M.A., 75 (2012), 3836.
doi: 10.1016/j.na.2012.02.005. |
[5] |
P. Caldiroli and R. Musina, On Caffarelli-Kohn-Nirenberg type inequalities for the weighted biharmonic operator in cones,, Milan J. Math., 79 (2011), 657.
doi: 10.1007/s00032-011-0167-2. |
[6] |
P. Caldiroli and R. Musina, A class of second order dilation invariant inequalities,, in, (). Google Scholar |
[7] |
F. Catrina and Z.-Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions,, Comm. Pure Appl. Math., 54 (2001), 229.
doi: 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I. |
[8] |
N. Ghoussoub and A. Moradifam, Bessel pairs and optimal Hardy and Hardy-Rellich inequalities,, Math. Ann., 349 (2011), 1.
doi: 10.1007/s00208-010-0510-x. |
[9] |
N. Ghoussoub and A. Moradifam, "Functional Inequalities: New Perspectives and New Applications,", Mathematical Surveys and Monographs, (2013).
|
[10] |
C.-S. Lin, Interpolation inequalities with weights,, Comm. Part. Diff. Eq., 11 (1986), 1515.
doi: 10.1080/03605308608820473. |
[11] |
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The Limit Case, Part 1,, Rev. Mat. Iberoam., 1 (1985), 145.
doi: 10.4171/RMI/6. |
[12] |
E. Mitidieri, A Rellich type identity and applications,, Comm. Part. Diff. Eq., 18 (1993), 125.
doi: 10.1080/03605309308820923. |
[13] |
E. Mitidieri, Nonexistence of positive solutions of semilinear elliptic systems in $\R^N$,, Diff. Int. Eq., 9 (1996), 465.
|
[14] |
A. Moradifam, Optimal weighted Hardy-Rellich inequalities on $H^2 \cap H^1_0$,, J. London. Math. Soc., 85 (2011), 22.
doi: 10.1112/jlms/jdr045. |
[15] |
R. Musina, Weighted Sobolev spaces of radially symmetric functions,, Ann. Mat. Pura Appl., ().
doi: 10.1007/s10231-013-0348-4. |
[16] |
E. S. Noussair, C. A. Swanson and J. Yang, Transcritical Biharmonic Equations in $R^N$,, Funkcialaj Ekvacioj, 35 (1992), 533.
|
[17] |
F. Rellich, Halbbeschränkte Differentialoperatoren höherer Ordnung,, in, (1954), 243.
|
[18] |
F. Rellich, "Perturbation Theory of Eigenvalue Problems,", Gordon and Breach, (1969).
|
[19] |
M. Struwe, "Variational Methods,", fourth edition, (2008).
doi: PMCid:PMC2582268. |
[20] |
C. A. Swanson, The best Sobolev constant,, Appl. Anal., 47 (1992), 227.
doi: 10.1080/00036819208840142. |
[21] |
S. Terracini, On positive entire solutions to a class of equations with a singular coefficient and critical exponent,, Adv. Differential Eq., 1 (1996), 241.
|
[22] |
A. Tertikas and N. B. Zographopoulos, Best constants in the Hardy-Rellich inequalities and related improvements,, Adv. Math., 209 (2007), 407.
doi: 10.1016/j.aim.2006.05.011. |
show all references
References:
[1] |
Adimurthi, M. Grossi and S. Santra, Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem,, J. Funct. Anal., 240 (2006), 36.
doi: 10.1016/j.jfa.2006.07.011. |
[2] |
Adimurthi and S. Santra, Generalized Hardy-Rellich inequalities in critical dimensions and its applications,, Commun. Contemp. Math., 11 (2009), 367.
doi: 10.1142/S0219199709003405. |
[3] |
C. O. Alves and J. M. do Ò, Positive solutions of a fourth-order semilinear problem involving critical growth,, Adv. Nonlinear Stud., 2 (2002), 437.
|
[4] |
M. Bhakta and R. Musina, Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials,, Nonlinear Anal. T.M.A., 75 (2012), 3836.
doi: 10.1016/j.na.2012.02.005. |
[5] |
P. Caldiroli and R. Musina, On Caffarelli-Kohn-Nirenberg type inequalities for the weighted biharmonic operator in cones,, Milan J. Math., 79 (2011), 657.
doi: 10.1007/s00032-011-0167-2. |
[6] |
P. Caldiroli and R. Musina, A class of second order dilation invariant inequalities,, in, (). Google Scholar |
[7] |
F. Catrina and Z.-Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions,, Comm. Pure Appl. Math., 54 (2001), 229.
doi: 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I. |
[8] |
N. Ghoussoub and A. Moradifam, Bessel pairs and optimal Hardy and Hardy-Rellich inequalities,, Math. Ann., 349 (2011), 1.
doi: 10.1007/s00208-010-0510-x. |
[9] |
N. Ghoussoub and A. Moradifam, "Functional Inequalities: New Perspectives and New Applications,", Mathematical Surveys and Monographs, (2013).
|
[10] |
C.-S. Lin, Interpolation inequalities with weights,, Comm. Part. Diff. Eq., 11 (1986), 1515.
doi: 10.1080/03605308608820473. |
[11] |
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The Limit Case, Part 1,, Rev. Mat. Iberoam., 1 (1985), 145.
doi: 10.4171/RMI/6. |
[12] |
E. Mitidieri, A Rellich type identity and applications,, Comm. Part. Diff. Eq., 18 (1993), 125.
doi: 10.1080/03605309308820923. |
[13] |
E. Mitidieri, Nonexistence of positive solutions of semilinear elliptic systems in $\R^N$,, Diff. Int. Eq., 9 (1996), 465.
|
[14] |
A. Moradifam, Optimal weighted Hardy-Rellich inequalities on $H^2 \cap H^1_0$,, J. London. Math. Soc., 85 (2011), 22.
doi: 10.1112/jlms/jdr045. |
[15] |
R. Musina, Weighted Sobolev spaces of radially symmetric functions,, Ann. Mat. Pura Appl., ().
doi: 10.1007/s10231-013-0348-4. |
[16] |
E. S. Noussair, C. A. Swanson and J. Yang, Transcritical Biharmonic Equations in $R^N$,, Funkcialaj Ekvacioj, 35 (1992), 533.
|
[17] |
F. Rellich, Halbbeschränkte Differentialoperatoren höherer Ordnung,, in, (1954), 243.
|
[18] |
F. Rellich, "Perturbation Theory of Eigenvalue Problems,", Gordon and Breach, (1969).
|
[19] |
M. Struwe, "Variational Methods,", fourth edition, (2008).
doi: PMCid:PMC2582268. |
[20] |
C. A. Swanson, The best Sobolev constant,, Appl. Anal., 47 (1992), 227.
doi: 10.1080/00036819208840142. |
[21] |
S. Terracini, On positive entire solutions to a class of equations with a singular coefficient and critical exponent,, Adv. Differential Eq., 1 (1996), 241.
|
[22] |
A. Tertikas and N. B. Zographopoulos, Best constants in the Hardy-Rellich inequalities and related improvements,, Adv. Math., 209 (2007), 407.
doi: 10.1016/j.aim.2006.05.011. |
[1] |
Alexey Yulin, Alan Champneys. Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1341-1357. doi: 10.3934/dcdss.2011.4.1341 |
[2] |
Wei Liu, Pavel Krejčí, Guoju Ye. Continuity properties of Prandtl-Ishlinskii operators in the space of regulated functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3783-3795. doi: 10.3934/dcdsb.2017190 |
[3] |
Alexandre B. Simas, Fábio J. Valentim. $W$-Sobolev spaces: Higher order and regularity. Communications on Pure & Applied Analysis, 2015, 14 (2) : 597-607. doi: 10.3934/cpaa.2015.14.597 |
[4] |
Charles Fulton, David Pearson, Steven Pruess. Characterization of the spectral density function for a one-sided tridiagonal Jacobi matrix operator. Conference Publications, 2013, 2013 (special) : 247-257. doi: 10.3934/proc.2013.2013.247 |
[5] |
A. Aghajani, S. F. Mottaghi. Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities. Communications on Pure & Applied Analysis, 2018, 17 (3) : 887-898. doi: 10.3934/cpaa.2018044 |
[6] |
Yimin Zhang, Youjun Wang, Yaotian Shen. Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1037-1054. doi: 10.3934/cpaa.2011.10.1037 |
[7] |
Andrea Cianchi, Adele Ferone. Improving sharp Sobolev type inequalities by optimal remainder gradient norms. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1363-1386. doi: 10.3934/cpaa.2012.11.1363 |
[8] |
Hirofumi Notsu, Masato Kimura. Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity. Networks & Heterogeneous Media, 2014, 9 (4) : 617-634. doi: 10.3934/nhm.2014.9.617 |
[9] |
Ademir Fernando Pazoto, Lionel Rosier. Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the half-line. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1511-1535. doi: 10.3934/dcdsb.2010.14.1511 |
2019 Impact Factor: 1.105
Tools
Metrics
Other articles
by authors
[Back to Top]