Harnack Inequality and Applications to Solutions of Biharmonic Equations
We prove Harnack type inequalities for linear biharmonic equations containing a Kato potential. Various applications to local boundedness, Hölder continuity and universal estimates of solutions for biharmonic equations are presented.
KeywordsWeak Solution Green Function Elliptic System Harnack Inequality Biharmonic Equation
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- I. Bachar, H. Mâagli, and L. Mâatoug, Positive solutions of nonlinear elliptic equations in a half-space in ℝ2, Electronic Journal of Differential Equations, Vol. 2002(2002), No. 41, pp. 1–24.Google Scholar
- I. Bachar, H. Mâagli, and M. Zribi, Existence of positive solutions to nonlinear elliptic problem in the half space, Electronic Journal of Differential Equations, Vol. 2005 (2005), No. 44, pp. 1–16.Google Scholar
- M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Annals of Mathematics Studies, Princeton University Press, 1983.Google Scholar
- D. Gilbarg, N. Trudinger, Elliptic partial differential equations of second order, Springer Verlag, 1983.Google Scholar
- E. Mitidieri, S.I. Pohozaev, A priori estimates and nonexistence of solutions to nonlinear partial differential equations and inequalities, Tr. Math. Inst. Steklova, Ross. Akad. Nauk, vol. 234, 2001.Google Scholar
- M. Nicolescu, Les Fonctions Polyharmoniques, Hermann and Cie Editeurs, Paris 1936.Google Scholar
- M. Schechter, Spectra of partial differential operators, North-Holland, 1986.Google Scholar