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Remarks on the regularity of weak solutions to some variational inequalities

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References

  1. Biroli, M., DeGiorgi-Nash: Moser result for a variational inequality. Boll. UMI (5)16-A, 598–605 (1979)

    Google Scholar 

  2. Boccardo, L.: AnL s-estimate for the gradient of solutions of some strongly nonlinear unilateral problem, pre-print

  3. Brezis, H.: Equations of inéquations non linéaires dans les espaces vectoriels en dualité. Ann. Inst. Fourier18, 115–175 (1968)

    Google Scholar 

  4. Brezis, H., Kinderlehrer, D.: The smoothness of solutions to nonlinear variational inequalities. Indiana J. Math.23, 831–844 (1974)

    Google Scholar 

  5. Brezis, H., Stampacchia, G.: Sur la régularité de la solution d'inéquations elliptiques. Bull. Soc. Math. France96, 153–180 (1968)

    Google Scholar 

  6. Campanato, S.: Proprietà di holderianità di alcune classi di funzioni. Ann. S. N. Sup. Pisa17 (1963)

  7. Campanato, S.: Proprietà di una famiglia di spazi funzionali. Ann. S.N. Sup. Pisa18 (1964)

  8. Campanato, S.: Equazioni ellittiche del II ordine e spazi ℒ2,λ. Ann. Mat. Pura e Appl.69, 321–382 (1965)

    Google Scholar 

  9. Campanato, S.: Equazioni ellittiche non variazionali a coefficienti continui. Ann. Mat. Pura e Appl.86 (1970)

  10. Campanato, S.: Equazioni paraboliche del secondo ordine e spazi ℒ2,θ(Ω, δ. Ann. Mat. Pure eAppl.73, 55–102 (1966)

    Google Scholar 

  11. Frehse, J.: On the regularity of the solution of a second order variational inequality. Boll. U.M.I.6 (1972)

  12. Frehse, J., Mosco, U.: Variational inequalities with one-sided irregular obstacles. Manuscripta Math.28, 219–234 (1979)

    Google Scholar 

  13. Gerhardt, C.: Regularity of solutions of non linear variational inequalities. Arch. Rat. Mech. Anal.52, 389–393 (1973)

    Google Scholar 

  14. Giaquinta, M.: Sistemi ellittici non lineari. Teoria della regolarità. Boll. U.M.I.16-A, 259–283 (1979)

    Google Scholar 

  15. Giaquinta, M.: Regularity results for weak solutions to variational equations and inequalities fornon linear elliptic systems and for weak solutions to non linear parabolic systems. Pre-print Sonderforschungsbereich 123, Univ. Heidelberg (1980)

  16. Giaquinta, M.: A note on the higher integrability from reverse Holder inequality. Pre-print Seminari Ist. Mat. Applicata Firenze (1979)

  17. Giaquinta, M., Giusti, E.: Nonlinear elliptic systems with quadratic growth. Manuscripta Math.24, 323–349 (1978)

    Google Scholar 

  18. Giaquinta, M., Modica, G.: Regularity results for some classes of higher order non linear elliptic systems. To appear in J. für Reine und Angewandte Math.

  19. Giaquinta, M., Modica, G.: Almost everywhere regularity results for solutions of non linear elliptic systems. Manuscripta Math.28, 109–158 (1979)

    Google Scholar 

  20. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  21. Hildebrandt, S., Widman, K.-O.: Some regularity results for quasilinear elliptic systems of second order. Math. Z.142, 67–86 (1975)

    Google Scholar 

  22. Hildebrandt, S., Widman, K-O.: Variational inequalities for vector valued functions. To appear in J. für Reine und Angewandte Math.

  23. Kinderlehrer, D.: Variational inequalities and free boudary problems. Bull. A.M.S.84, 7–26 (1978)

    Google Scholar 

  24. Kufner, A., John, O., Fučik, S.: Functions spaces. Prague 1977

  25. Ladyzenskaya, O.A., Ural'tseva, N.N.: Linear and quasilinear elliptic equations. New York: Academic Press 1968

    Google Scholar 

  26. Lewy, H.: On a variational problem with inequalities on the boundary. J. of Math. and Mech.17, 861–884 (1968)

    Google Scholar 

  27. Lewy, H., Stampacchia, G.: On the regularity of the solution of a variational inequality. Comm. Pure and Appl. Math.22, 153–188 (1969)

    Google Scholar 

  28. Lions, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris: Dunod 1969

    Google Scholar 

  29. Lions, J.L., Stampacchia, G.: Variational inequalities. Comm. Pure and Appl. Math.20, 493–519 (1967)

    Google Scholar 

  30. Morrey, C.B.: Multiple integrals in the Calculus of Variations. Berlin Heidelberg New York: Springer 1966

    Google Scholar 

  31. Serrin, J.: Local behavior of solutions of quasilinear equations. Acta Math.11, 247–302 (1964)

    Google Scholar 

  32. Stampacchia, G.: Formes bilinéaires coercitives sur les ensemble convex. C.R.Ac.Sc. Paris258, 4413–4416 (1964)

    Google Scholar 

  33. Stampacchia, G.: Equations elliptiques du second ordre à coefficients discontinues. Les Presses de l'Université de Montréal (1966)

  34. Uhlenbeck, K.: Regularity for a class of non-linear elliptic systems. Acta Math. (1977)

  35. Beirao da Veiga, U.: Sur la regularité des solutions de l'équation divA(x,u,∇u) =B(x,u,∇u) avec des conditions aux limites unilaterales et mêlées. Ann. Mat. Pura e Appl.64 (1973)

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Giaquinta, M. Remarks on the regularity of weak solutions to some variational inequalities. Math Z 177, 15–31 (1981). https://doi.org/10.1007/BF01214336

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