Cao, Daomin; Wan, Jie; Zhan, Weicheng Desingularization of vortex rings in 3 dimensional Euler flows. (English) Zbl 1451.35120 J. Differ. Equations 270, 1258-1297 (2021). MSC: 35Q31 76B47 35B40 PDF BibTeX XML Cite \textit{D. Cao} et al., J. Differ. Equations 270, 1258--1297 (2021; Zbl 1451.35120) Full Text: DOI
Rebah, D. Steady vortex rings in a uniform flow and rearrangements of a function. (English) Zbl 1433.49064 Result. Math. 75, No. 1, Paper No. 23, 19 p. (2020). MSC: 49S05 76B47 46E30 49J05 PDF BibTeX XML Cite \textit{D. Rebah}, Result. Math. 75, No. 1, Paper No. 23, 19 p. (2020; Zbl 1433.49064) Full Text: DOI
Wang, Bo; Bao, Jiguang Over-determined problems for \(k\)-Hessian equations in ring-shaped domains. (English) Zbl 1330.35274 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 127, 143-156 (2015). MSC: 35N05 PDF BibTeX XML Cite \textit{B. Wang} and \textit{J. Bao}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 127, 143--156 (2015; Zbl 1330.35274) Full Text: DOI
Zhang, Yan; Danaila, Ionut Existence and numerical modelling of vortex rings with elliptic boundaries. (English) Zbl 1438.76009 Appl. Math. Modelling 37, No. 7, 4809-4824 (2013). MSC: 76B47 35J65 35R05 35R35 65N30 76M10 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{I. Danaila}, Appl. Math. Modelling 37, No. 7, 4809--4824 (2013; Zbl 1438.76009) Full Text: DOI
de Valeriola, Sébastien; Van Schaftingen, Jean Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem. (English) Zbl 1294.35083 Arch. Ration. Mech. Anal. 210, No. 2, 409-450 (2013). MSC: 35Q31 76B47 76B03 76B15 35J61 PDF BibTeX XML Cite \textit{S. de Valeriola} and \textit{J. Van Schaftingen}, Arch. Ration. Mech. Anal. 210, No. 2, 409--450 (2013; Zbl 1294.35083) Full Text: DOI arXiv
Fragalà, Ilaria; Gazzola, Filippo Partially overdetermined elliptic boundary value problems. (English) Zbl 1156.35049 J. Differ. Equations 245, No. 5, 1299-1322 (2008). MSC: 35J70 35J65 35B50 PDF BibTeX XML Cite \textit{I. Fragalà} and \textit{F. Gazzola}, J. Differ. Equations 245, No. 5, 1299--1322 (2008; Zbl 1156.35049) Full Text: DOI
Sirakov, Boyan Symmetry for exterior elliptic problems and two conjectures in potential theory. (English) Zbl 0997.35014 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No. 2, 135-156 (2001). MSC: 35J45 35Q72 31B15 PDF BibTeX XML Cite \textit{B. Sirakov}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No. 2, 135--156 (2001; Zbl 0997.35014) Full Text: DOI Numdam EuDML
Elcrat, Alan R.; Miller, Kenneth G. A monotone iteration for concentrated vortices. (English) Zbl 1160.35490 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 6, 777-789 (2001). Reviewer: Erich Miersemann (Leipzig)(MR1825781) MSC: 35P30 35A35 76B47 PDF BibTeX XML Cite \textit{A. R. Elcrat} and \textit{K. G. Miller}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 44, No. 6, 777--789 (2001; Zbl 1160.35490) Full Text: DOI Link
Hamel, François; Monneau, Régis Solutions of semilinear elliptic equations in \(\mathbb{R}^N\) with conical-shaped level sets. (English) Zbl 0952.35041 Commun. Partial Differ. Equations 25, No. 5-6, 769-819 (2000). Reviewer: Dmitry V.Larin (Donetsk) MSC: 35J60 35B05 35A05 PDF BibTeX XML Cite \textit{F. Hamel} and \textit{R. Monneau}, Commun. Partial Differ. Equations 25, No. 5--6, 769--819 (2000; Zbl 0952.35041) Full Text: DOI
Buffoni, B. Nested axi-symmetric vortex rings. (English) Zbl 0902.76019 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 14, No. 6, 787-797 (1997). Reviewer: F.Kaplanski (Tallinn) MSC: 76B47 35Q35 PDF BibTeX XML Cite \textit{B. Buffoni}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 14, No. 6, 787--797 (1997; Zbl 0902.76019) Full Text: DOI Numdam EuDML
Yang, Jianfu Global vortex rings and asymptotic behaviour. (English) Zbl 0845.76017 Nonlinear Anal., Theory Methods Appl. 25, No. 5, 531-546 (1995). Reviewer: A.Berezovski (Tallinn) MSC: 76B47 35Q35 PDF BibTeX XML Cite \textit{J. Yang}, Nonlinear Anal., Theory Methods Appl. 25, No. 5, 531--546 (1995; Zbl 0845.76017) Full Text: DOI
Tadie On the bifurcation of steady vortex rings from a Green function. (English) Zbl 0853.35135 Math. Proc. Camb. Philos. Soc. 116, No. 3, 555-568 (1994). Reviewer: V.A.Sava (Iaşi) MSC: 35R35 76B47 PDF BibTeX XML Cite \textit{Tadie}, Math. Proc. Camb. Philos. Soc. 116, No. 3, 555--568 (1994; Zbl 0853.35135) Full Text: DOI
Douglas, R. J. Rearrangements of functions on unbounded domains. (English) Zbl 0818.49010 Proc. R. Soc. Edinb., Sect. A 124, No. 4, 621-644 (1994). Reviewer: G.Stefani (Firenze) MSC: 49J40 26A99 28D05 76B47 PDF BibTeX XML Cite \textit{R. J. Douglas}, Proc. R. Soc. Edinb., Sect. A, Math. 124, No. 4, 621--644 (1994; Zbl 0818.49010) Full Text: DOI
Kloeden, P. E. The uniqueness of classes of explicit solutions of boundary value problems. (English) Zbl 0806.35141 Math. Comput. Modelling 18, No. 10, 107-109 (1993). MSC: 35Q35 76B47 PDF BibTeX XML Cite \textit{P. E. Kloeden}, Math. Comput. Modelling 18, No. 10, 107--109 (1993; Zbl 0806.35141) Full Text: DOI
del Pino, Manuel A. A global estimate for the gradient in a singular elliptic boundary value problem. (English) Zbl 0791.35046 Proc. R. Soc. Edinb., Sect. A, Math. 122, No. 3-4, 341-352 (1992). Reviewer: E.Mascolo (Firenze) MSC: 35J65 35A05 35B45 PDF BibTeX XML Cite \textit{M. A. del Pino}, Proc. R. Soc. Edinb., Sect. A, Math. 122, No. 3--4, 341--352 (1992; Zbl 0791.35046) Full Text: DOI
Ambrosetti, Antonio Critical points and nonlinear variational problems. (English) Zbl 0766.49006 Mém. Soc. Math. Fr., Nouv. Sér. 49, 139 p. (1992). Reviewer: J.F.Bonnans (Le Chesnay) MSC: 49J20 49J15 PDF BibTeX XML Cite \textit{A. Ambrosetti}, Mém. Soc. Math. Fr., Nouv. Sér. 49, 139 p. (1992; Zbl 0766.49006) Full Text: DOI Numdam EuDML
Fraenkel, L. E. The capacity of slender toroidal sets in \({\mathbb{R}{}}^ N\). (English) Zbl 0755.31005 Arch. Ration. Mech. Anal. 118, No. 2, 169-193 (1992). Reviewer: V.Ionescu (Bucureşti) MSC: 31B15 35J20 35R35 PDF BibTeX XML Cite \textit{L. E. Fraenkel}, Arch. Ration. Mech. Anal. 118, No. 2, 169--193 (1992; Zbl 0755.31005) Full Text: DOI
Ambrosetti, Antonio; Struwe, Michael Existence of steady vortex rings in an ideal fluid. (English) Zbl 0709.35081 Appl. Math. Lett. 2, No. 2, 183-186 (1989). MSC: 35Q35 76B47 35J65 PDF BibTeX XML Cite \textit{A. Ambrosetti} and \textit{M. Struwe}, Appl. Math. Lett. 2, No. 2, 183--186 (1989; Zbl 0709.35081) Full Text: DOI
Berestycki, Henri; Pacella, Filomena Symmetry properties for positive solutions of elliptic equations with mixed boundary conditions. (English) Zbl 0706.35021 J. Funct. Anal. 87, No. 1, 177-211 (1989). MSC: 35B99 35J65 PDF BibTeX XML Cite \textit{H. Berestycki} and \textit{F. Pacella}, J. Funct. Anal. 87, No. 1, 177--211 (1989; Zbl 0706.35021) Full Text: DOI
Ambrosetti, A.; Struwe, M. Existence of steady vortex rings in an ideal fluid. (English) Zbl 0694.76012 Arch. Ration. Mech. Anal. 108, No. 2, 97-109 (1989). MSC: 76B47 35Q30 PDF BibTeX XML Cite \textit{A. Ambrosetti} and \textit{M. Struwe}, Arch. Ration. Mech. Anal. 108, No. 2, 97--109 (1989; Zbl 0694.76012) Full Text: DOI
Berestycki, H.; Nirenberg, L. Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations. (English) Zbl 0698.35031 J. Geom. Phys. 5, No. 2, 237-275 (1988). Reviewer: P.-L.Lions MSC: 35B99 35J60 35K55 35B50 PDF BibTeX XML Cite \textit{H. Berestycki} and \textit{L. Nirenberg}, J. Geom. Phys. 5, No. 2, 237--275 (1988; Zbl 0698.35031) Full Text: DOI
Amick, C. J.; Fraenkel, L. E. The uniqueness of a family of steady vortex rings. (English) Zbl 0694.76011 Arch. Ration. Mech. Anal. 100, No. 3, 207-241 (1988). MSC: 76B47 35Q99 PDF BibTeX XML Cite \textit{C. J. Amick} and \textit{L. E. Fraenkel}, Arch. Ration. Mech. Anal. 100, No. 3, 207--241 (1988; Zbl 0694.76011) Full Text: DOI
Burton, G. R. Vortex rings in a cylinder and rearrangements. (English) Zbl 0648.35029 J. Differ. Equations 70, 333-348 (1987). Reviewer: B.Kawohl MSC: 35J20 76B47 PDF BibTeX XML Cite \textit{G. R. Burton}, J. Differ. Equations 70, 333--348 (1987; Zbl 0648.35029) Full Text: DOI
Keady, G.; Kloeden, P. E. An elliptic boundary-value problem with a discontinuous nonlinearity. II. (English) Zbl 0647.35029 Proc. R. Soc. Edinb., Sect. A 105, 23-36 (1987). MSC: 35J65 35R05 35B40 PDF BibTeX XML Cite \textit{G. Keady} and \textit{P. E. Kloeden}, Proc. R. Soc. Edinb., Sect. A, Math. 105, 23--36 (1987; Zbl 0647.35029) Full Text: DOI
Burton, G. R. Rearrangements of functions, maximization of convex functionals, and vortex rings. (English) Zbl 0592.35049 Math. Ann. 276, 225-253 (1987). MSC: 35J60 76B47 49K20 PDF BibTeX XML Cite \textit{G. R. Burton}, Math. Ann. 276, 225--253 (1987; Zbl 0592.35049) Full Text: DOI EuDML