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Volumn 254, Issue 1, 2006, Pages 117-132

Overdetermined problems with possibly degenerate ellipticity, a geometric approach

Author keywords

Degenerate elliptic operators; Overdetermined boundary value problem

Indexed keywords


EID: 33745838959     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-006-0937-7     Document Type: Article
Times cited : (79)

References (38)
  • 2
    • 0000683727 scopus 로고
    • A characteristic property of the spheres
    • Alexandrov, A.D.: A characteristic property of the spheres. Ann. Mat. Pura Appl. 58, 303-354 (1962)
    • (1962) Ann. Mat. Pura Appl. , vol.58 , pp. 303-354
    • Alexandrov, A.D.1
  • 3
    • 0034422387 scopus 로고    scopus 로고
    • Solitons in several space dimensions: Derrick's problem and infinitely many solutions
    • Benci, V., D'Avenia, P., Fortunate, D., Pisani, L.: Solitons in several space dimensions: Derrick's problem and infinitely many solutions. Arch. Ration. Mech. Anal. 154, 297-324 (2000)
    • (2000) Arch. Ration. Mech. Anal. , vol.154 , pp. 297-324
    • Benci, V.1    D'Avenia, P.2    Fortunate, D.3    Pisani, L.4
  • 4
    • 0032222023 scopus 로고    scopus 로고
    • Soliton like solutions of a Lorentz invariant equation in dimension 3
    • Beuci, V., Fortunate, D., Pisani, L.: Soliton like solutions of a Lorentz invariant equation in dimension 3. Rev. Math. Phys. 10, 315-344 (1998)
    • (1998) Rev. Math. Phys. , vol.10 , pp. 315-344
    • Beuci, V.1    Fortunate, D.2    Pisani, L.3
  • 6
    • 33745823636 scopus 로고    scopus 로고
    • A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative
    • Brock, F., Henrot, A.: A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative. Rend. Circ. Mat. Palermo 51, 375-390 (2002)
    • (2002) Rend. Circ. Mat. Palermo , vol.51 , pp. 375-390
    • Brock, F.1    Henrot, A.2
  • 7
    • 84945016371 scopus 로고
    • Minimal rearrangements of Sobolev functions
    • Brothers, I.E., Ziemer, W.P.: Minimal rearrangements of Sobolev functions. J. Reine Angew. Math. 384, 153-179 (1988)
    • (1988) J. Reine Angew. Math. , vol.384 , pp. 153-179
    • Brothers, I.E.1    Ziemer, W.P.2
  • 9
    • 20344362744 scopus 로고
    • A lower bound for the smallest eigenvalue of the Laplacian
    • Princeton Univ. Press
    • Cheeger, J.: A lower bound for the smallest eigenvalue of the Laplacian. In: Problems in Analysis (Papers dedicated to Salomon Bochner), pp. 195-199. Princeton Univ. Press. 1970
    • (1970) Problems in Analysis (Papers Dedicated to Salomon Bochner) , pp. 195-199
    • Cheeger, J.1
  • 10
    • 0002509241 scopus 로고    scopus 로고
    • Use of the domain derivative to prove symmetry results in partial differential equations
    • Choulli, M., Henrot, A.: Use of the domain derivative to prove symmetry results in partial differential equations. Math. Nachr. 192, 91-103 (1998)
    • (1998) Math. Nachr. , vol.192 , pp. 91-103
    • Choulli, M.1    Henrot, A.2
  • 11
    • 31644432113 scopus 로고    scopus 로고
    • A symmetry problem in the calculus of variations
    • Crasta, G.: A symmetry problem in the calculus of variations. J.Europ. Math. Soc. 8, 139-154 (2006)
    • (2006) J.Europ. Math. Soc. , vol.8 , pp. 139-154
    • Crasta, G.1
  • 12
    • 33645629468 scopus 로고
    • Comments on nonlinear wave equations as models for elementary particles
    • Derrick, G.H.: Comments on nonlinear wave equations as models for elementary particles. J. Math. Phys. 5, 1252-1254 (1964)
    • (1964) J. Math. Phys. , vol.5 , pp. 1252-1254
    • Derrick, G.H.1
  • 13
    • 0010864095 scopus 로고    scopus 로고
    • Monotonicity and symmetry results for p-Laplace equations and applications
    • Damascelli, L., Pacella, F.: Monotonicity and symmetry results for p-Laplace equations and applications. Adv. Differential Equations 5, 1179-1200 (2000)
    • (2000) Adv. Differential Equations , vol.5 , pp. 1179-1200
    • Damascelli, L.1    Pacella, F.2
  • 14
    • 0036851034 scopus 로고    scopus 로고
    • Born-Infeld type equations for electrostatic fields
    • Fortunato, D., Orsina, L., Pisani, L.: Born-Infeld type equations for electrostatic fields. J. Math. Phys. 43, 5698-5706 (2002)
    • (2002) J. Math. Phys. , vol.43 , pp. 5698-5706
    • Fortunato, D.1    Orsina, L.2    Pisani, L.3
  • 15
    • 0002964419 scopus 로고
    • A symmetry result related to some overdetermined boundary value problems
    • Garofalo, N., Lewis, J.L.: A symmetry result related to some overdetermined boundary value problems. Amer. J. Math. 111, 9-33 (1989)
    • (1989) Amer. J. Math. , vol.111 , pp. 9-33
    • Garofalo, N.1    Lewis, J.L.2
  • 16
    • 0013038125 scopus 로고    scopus 로고
    • Symmetry in exterior boundary value problems for quasilinear elliptic equations via blow-up and a priori estimates
    • Garofalo, N., Sartori, E.: Symmetry in exterior boundary value problems for quasilinear elliptic equations via blow-up and a priori estimates. Adv. Diff. Eq. 4, 137-161 (1999)
    • (1999) Adv. Diff. Eq. , vol.4 , pp. 137-161
    • Garofalo, N.1    Sartori, E.2
  • 17
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • Gidas, B., Ni, W.M., Nirenberg, L.: Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68, 209-243 (1979)
    • (1979) Comm. Math. Phys. , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.M.2    Nirenberg, L.3
  • 20
    • 0003269816 scopus 로고
    • Rearrangements and convexity of level sets in PDE
    • Kawohl, B.: Rearrangements and Convexity of Level Sets in PDE. Springer Lecture Notes in Math. 1150, (1985)
    • (1985) Springer Lecture Notes in Math. , vol.1150
    • Kawohl, B.1
  • 21
    • 0002861534 scopus 로고
    • On a family of torsional creep problems
    • Kawohl, B.: On a family of torsional creep problems. J. Reine Angew. Math. 410, 1-22 (1990)
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 1-22
    • Kawohl, B.1
  • 23
    • 27944507242 scopus 로고    scopus 로고
    • Symmetrization - Or how to prove symmetry of solutions to partial differential equations
    • Jäger, W., Nečas, J., John, O., Najzar, K., Stara, J (eds) Partial Differential Equations, Theory and Numerical Solution, London
    • Kawohl, B.: Symmetrization - or how to prove symmetry of solutions to partial differential equations. In: Jäger, W., Nečas, J., John, O., Najzar, K., Stara, J (eds) Partial Differential Equations, Theory and Numerical Solution, Chapman & Hall CRC Research Notes in Math. 406, London, 1999, pp. 214-229
    • (1999) Chapman & Hall CRC Research Notes in Math. , vol.406 , pp. 214-229
    • Kawohl, B.1
  • 24
    • 85068234417 scopus 로고    scopus 로고
    • Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant
    • Kawohl, B., Fridman, V.: Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant. Comment. Math. Univ. Carol. 44, 659-667 (2003)
    • (2003) Comment. Math. Univ. Carol. , vol.44 , pp. 659-667
    • Kawohl, B.1    Fridman, V.2
  • 25
    • 33745822560 scopus 로고    scopus 로고
    • Characterization of Cheeger sets for convex subsets of the plane
    • to appear
    • Kawohl, B., Lachand-Robert, T.: Characterization of Cheeger sets for convex subsets of the plane. Pacific J. Math, to appear
    • Pacific J. Math
    • Kawohl, B.1    Lachand-Robert, T.2
  • 26
    • 0034405316 scopus 로고    scopus 로고
    • Electrostatic characterization of spheres
    • Mendez, O., Reichel, W.: Electrostatic characterization of spheres. Forum Math. 12, 223-245 (2000)
    • (2000) Forum Math. , vol.12 , pp. 223-245
    • Mendez, O.1    Reichel, W.2
  • 27
    • 0001378784 scopus 로고
    • Compact hypersurfaces: The Alexandrov theorem for higher order mean curvatures
    • Differential Geometry, Longman Sci. Tech.
    • Montiel, S., Ros, A.: Compact hypersurfaces: the Alexandrov theorem for higher order mean curvatures. In: Differential Geometry, Pitman Monogr. Surveys Pure Appl. Math. 52, Longman Sci. Tech. 1991. pp. 279-296
    • (1991) Pitman Monogr. Surveys Pure Appl. Math. , vol.52 , pp. 279-296
    • Montiel, S.1    Ros, A.2
  • 28
    • 0000792894 scopus 로고
    • Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature
    • Payne, L.E., Philippin, G.A.: Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature. Nonlinear Anal. 3, 193-211 (1979)
    • (1979) Nonlinear Anal. , vol.3 , pp. 193-211
    • Payne, L.E.1    Philippin, G.A.2
  • 29
    • 0000781260 scopus 로고
    • On the largest possible circle imbedded in a given closed curve
    • in Russian
    • Pestov, G., Ionin, V.: On the largest possible circle imbedded in a given closed curve. Doklady Akad. Nauk. SSSR 127, 1170-1172 (1959) (in Russian)
    • (1959) Doklady Akad. Nauk. SSSR , vol.127 , pp. 1170-1172
    • Pestov, G.1    Ionin, V.2
  • 31
    • 0041169378 scopus 로고    scopus 로고
    • Serrin's result for domains with a comer or cusp
    • Prajapat, J.: Serrin's result for domains with a comer or cusp. Duke Math. J. 91, 29-31 (1998)
    • (1998) Duke Math. J. , vol.91 , pp. 29-31
    • Prajapat, J.1
  • 32
    • 0031335251 scopus 로고    scopus 로고
    • Radial symmetry for elliptic boundary value problems on exterior domains
    • Reichel, W.: Radial symmetry for elliptic boundary value problems on exterior domains. Arch. Ration. Mech. Anal. 137, 381-394 (1997)
    • (1997) Arch. Ration. Mech. Anal. , vol.137 , pp. 381-394
    • Reichel, W.1
  • 33
    • 0001168417 scopus 로고
    • On the strong maximum principle for quasilinear second order differential inequalities
    • Serrin, J.: On the strong maximum principle for quasilinear second order differential inequalities. J. Funct. Anal. 5, 184-193 (1970)
    • (1970) J. Funct. Anal. , vol.5 , pp. 184-193
    • Serrin, J.1
  • 34
    • 0001358147 scopus 로고
    • A symmetry problem in potential theory
    • Serrin, J.: A symmetry problem in potential theory. Arch. Ration. Mech. Anal. 43, 304-318 (1971)
    • (1971) Arch. Ration. Mech. Anal. , vol.43 , pp. 304-318
    • Serrin, J.1
  • 36
    • 0000962102 scopus 로고
    • Symmetry and regularity for general regions having a solution to certain over-determined boundary value problems
    • Vogel, A.L.: Symmetry and regularity for general regions having a solution to certain over-determined boundary value problems. Atti Sem. Mat. Fis. Univ. Modena 40, 443-484 (1992)
    • (1992) Atti Sem. Mat. Fis. Univ. Modena , vol.40 , pp. 443-484
    • Vogel, A.L.1
  • 37
    • 0001581915 scopus 로고
    • Remark on the preceding paper of Serrin
    • Weinberger, H.: Remark on the preceding paper of Serrin. Arch. Ration. Mech. Anal. 43, 319-320 (1971)
    • (1971) Arch. Ration. Mech. Anal. , vol.43 , pp. 319-320
    • Weinberger, H.1
  • 38
    • 84972492577 scopus 로고
    • The symmetry of sessile and pendent drops
    • Wente, H.C.: The symmetry of sessile and pendent drops. Pacific J. Math. 88, 387-397 (1980)
    • (1980) Pacific J. Math. , vol.88 , pp. 387-397
    • Wente, H.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.