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On linear and nonlinear elliptic boundary value problems in the plane with discontinuous coefficients
1. | D.I.M.E.T., Department of Computer Science, Mathematics, Electronics and Transportations, “Mediterranea” University of Reggio Calabria, 89060 Reggio Calabria, Italy, Italy |
References:
[1] |
L. Bers and L. Nirenberg, "On Linear and Non-Linear Elliptic Boundary Value Problems in the Plane," Atti del Convegno Internazionale sulle Equazioni lineari alle Derivate Parziali, Trieste, (1954), 141-167. |
[2] |
S. Campanato, Un risultato relativo ad equazioni ellittiche del secondo ordine di tipo non variazionale, Ann. Scuola Norm. Sup. Pisa (3), 21 (1967), 701-707. |
[3] |
S. Campanato, "Quaderni del Dottorato," Scuola Normale Superiore, Pisa, 1980. |
[4] |
S. Campanato, A maximum principle for nonlinear elliptic systems: Boundary fundamental estimates, Adv. Math., 66 (1987), 291-317.
doi: 10.1016/0001-8708(87)90037-5. |
[5] |
S. Campanato, Equazioni ellittiche del II ordine espazi $\mathcalL$$^(2, \lambda)$, Ann. Mat. Pura Appl., 69 (1965), 321-381.
doi: 10.1007/BF02414377. |
[6] |
E. De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3), 3 (1957), 25-43. |
[7] |
R. Finn and J. Serrin, On the Hölder continuity of quasi-conformal and elliptic mappings, Trans. Amer. Math. Soc., 89 (1958), 1-15. |
[8] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Reprint of the 1998 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2001. |
[9] |
S. Giuffrè, Oblique derivative problem for nonlinear elliptic discontinuous operators in the plane with quadratic growth, C. R. Acad. Sci. Paris Sér. I, Math., 328 (1999), 859-864. |
[10] |
S. Giuffrè, Global Hölder regularity for discontinuous elliptic equations in the plane, Proc. Amer. Math. Soc., 132 (2004), 1333-1344.
doi: 10.1090/S0002-9939-03-07348-9. |
[11] |
S. Giuffrè, Strong solvability of boundary value contact problems, Appl. Math. Optimization, 51 (2005), 361-372.
doi: 10.1007/s00245-004-0817-7. |
[12] |
S. Giuffrè and G. Idone, Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth, Journal of Global Optimization, 40 (2008), 99-117. |
[13] |
E. Giusti, Sulla regolarità delle soluzioni di una classe di equazioni ellittiche, Rend. Semin. Mat. Univ. Padova, 39 (1967), 362-375. |
[14] |
P. Hartman, Hölder continuity and non-linear elliptic partial differential equations, Duke Math. J., 25 (1957), 57-65.
doi: 10.1215/S0012-7094-58-02506-7. |
[15] |
A. Maugeri, D. K. Palagachev and L. Softova, "Elliptic and Parabolic Equations with Discontinuous Coefficients," Mathematical Research, 109, Wiley, VCH Verlag Berlin GmbH, Berlin, 2000. |
[16] |
C. B. Morrey Jr., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc., 43 (1938), 126-166.
doi: 10.1090/S0002-9947-1938-1501936-8. |
[17] |
L. Nirenberg, On nonlinear elliptic partial differential equations and Hölder continuity, Comm. Pure Appl. Math., 6 (1953), 103-156.
doi: 10.1002/cpa.3160060105. |
[18] |
D. K. Palagachev, Global strong solvability of Dirichlet problem for a class of nonlinear elliptic equations in the plane, Matematiche (Catania), 48 (1993), 311-321. |
[19] |
L. Softova, An integral estimate for the gradient for a class of nonlinear elliptic equations in the plane, Z. Anal. Anwen, 17 (1998), 57-66. |
[20] |
G. Talenti, Equazioni ellittiche in due variabili, Matematiche (Catania), 21 (1966), 339-376. |
[21] |
N. S. Trudinger, "Nonlinear Second Order Elliptic Equations," Lecture Notes of Math. Inst. of Nankai Univ., Tianjin, 1986. |
show all references
References:
[1] |
L. Bers and L. Nirenberg, "On Linear and Non-Linear Elliptic Boundary Value Problems in the Plane," Atti del Convegno Internazionale sulle Equazioni lineari alle Derivate Parziali, Trieste, (1954), 141-167. |
[2] |
S. Campanato, Un risultato relativo ad equazioni ellittiche del secondo ordine di tipo non variazionale, Ann. Scuola Norm. Sup. Pisa (3), 21 (1967), 701-707. |
[3] |
S. Campanato, "Quaderni del Dottorato," Scuola Normale Superiore, Pisa, 1980. |
[4] |
S. Campanato, A maximum principle for nonlinear elliptic systems: Boundary fundamental estimates, Adv. Math., 66 (1987), 291-317.
doi: 10.1016/0001-8708(87)90037-5. |
[5] |
S. Campanato, Equazioni ellittiche del II ordine espazi $\mathcalL$$^(2, \lambda)$, Ann. Mat. Pura Appl., 69 (1965), 321-381.
doi: 10.1007/BF02414377. |
[6] |
E. De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3), 3 (1957), 25-43. |
[7] |
R. Finn and J. Serrin, On the Hölder continuity of quasi-conformal and elliptic mappings, Trans. Amer. Math. Soc., 89 (1958), 1-15. |
[8] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," Reprint of the 1998 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2001. |
[9] |
S. Giuffrè, Oblique derivative problem for nonlinear elliptic discontinuous operators in the plane with quadratic growth, C. R. Acad. Sci. Paris Sér. I, Math., 328 (1999), 859-864. |
[10] |
S. Giuffrè, Global Hölder regularity for discontinuous elliptic equations in the plane, Proc. Amer. Math. Soc., 132 (2004), 1333-1344.
doi: 10.1090/S0002-9939-03-07348-9. |
[11] |
S. Giuffrè, Strong solvability of boundary value contact problems, Appl. Math. Optimization, 51 (2005), 361-372.
doi: 10.1007/s00245-004-0817-7. |
[12] |
S. Giuffrè and G. Idone, Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth, Journal of Global Optimization, 40 (2008), 99-117. |
[13] |
E. Giusti, Sulla regolarità delle soluzioni di una classe di equazioni ellittiche, Rend. Semin. Mat. Univ. Padova, 39 (1967), 362-375. |
[14] |
P. Hartman, Hölder continuity and non-linear elliptic partial differential equations, Duke Math. J., 25 (1957), 57-65.
doi: 10.1215/S0012-7094-58-02506-7. |
[15] |
A. Maugeri, D. K. Palagachev and L. Softova, "Elliptic and Parabolic Equations with Discontinuous Coefficients," Mathematical Research, 109, Wiley, VCH Verlag Berlin GmbH, Berlin, 2000. |
[16] |
C. B. Morrey Jr., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc., 43 (1938), 126-166.
doi: 10.1090/S0002-9947-1938-1501936-8. |
[17] |
L. Nirenberg, On nonlinear elliptic partial differential equations and Hölder continuity, Comm. Pure Appl. Math., 6 (1953), 103-156.
doi: 10.1002/cpa.3160060105. |
[18] |
D. K. Palagachev, Global strong solvability of Dirichlet problem for a class of nonlinear elliptic equations in the plane, Matematiche (Catania), 48 (1993), 311-321. |
[19] |
L. Softova, An integral estimate for the gradient for a class of nonlinear elliptic equations in the plane, Z. Anal. Anwen, 17 (1998), 57-66. |
[20] |
G. Talenti, Equazioni ellittiche in due variabili, Matematiche (Catania), 21 (1966), 339-376. |
[21] |
N. S. Trudinger, "Nonlinear Second Order Elliptic Equations," Lecture Notes of Math. Inst. of Nankai Univ., Tianjin, 1986. |
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