Global Solvability of Dirichlet Problem for Fully Nonlinear Elliptic Systems

REFERENCES

• S. Campanato ( 1989 ). A Cordes type condition for nonlinear variational systems . Rend Accad. Naz. Sci. XL, Mem. Mat. 13 : 307 – 321 .
   Google Scholar
• S. Campanato ( 1994 ). On the condition of nearness between operators . Ann. Mat. Pura Appl. 167 : 243 – 256 .
   Web of Science ®Google Scholar
• S. Campanato ( 1990 ). ℒ2, λ theory for nonlinear nonvariational differential systems . Rend. Mat. Appl. 10 : 531 – 549 .
   Google Scholar
• S. Campanato ( 1991 ). Nonvariational basic parabolic systems of second order . Rend. Accad. Naz. Lincei, Mat. Appl. 2 : 129 – 136 .
   Google Scholar
• L. Fattorusso and A. Tarsia ( 2013 ). Von Kármán equations in L p spaces . Appl. Anal. 92 : 2375 – 2391 .
   Web of Science ®Google Scholar
• D. Gilbarg and N. S. Trudinger ( 2001 ). Elliptic Partial Differential Equations of Second Order . [Reprint of the 1998 edition]. Classics in Mathematics. Springer-Verlag , Berlin .
   Google Scholar
• A. Granas and J. Dugundji ( 2003 ). Fixed Point Theory . Springer Monographs in Mathematics. Springer-Verlag , New York .
   Google Scholar
• A. Maugeri , D. K. Palagachev , and L. G. Softova ( 2002 ). Elliptic and Parabolic Equations with Discontinuous Coefficients. Mathematical Res. vol. 109 Wiley-VCH.
   Google Scholar
• D. K. Palagachev ( 1994 ). Global strong solvability of Dirichlet problem for a class of nonlinear elliptic equations in the plane . Matematiche (Catania) 48 : 311 – 321 .
   Google Scholar
• D. K. Palagachev ( 1995 ). Dirichlet problem for a class of second order nonlinear elliptic equations. Proceedings of the Fifth International Colloquium on Differential Equations (Plovdiv) pp. 273–282. .
   Google Scholar
• D. K. Palagachev , L. Recke , and L. G. Softova ( 2006 ). Applications of the differential calculus to nonlinear elliptic operators with discontinuous coefficients . Math. Ann. 336 : 617 – 637 .
   Web of Science ®Google Scholar
• L. Softova ( 1998 ). An integral estimate for the gradient for a class of nonlinear elliptic equations in the plane . Z. Anal. Anwendungen 17 : 57 – 66 .
   Google Scholar
• A. Tarsia ( 1996 ). Some topological properties preserved by nearness among operators and applications to PDE . Czechoslovak Math. J. 46 : 115 – 133 .
   Google Scholar
• A. Tarsia ( 1998 ). Differential equations and implicit functions: A generalization of “near operators” theorem . Topol. methods nonlinear Anal. 11 : 115 – 133 .
   Google Scholar
• A. Tarsia ( 2004 ). On Cordes and Campanato condition . Arch. Inequal. Appl. 2 : 25 – 39 .
   Google Scholar
• A. Tarsia ( 2008 ). Near operators theory and fully nonlinear elliptic equations . J. Global Optim. 40 : 443 – 453 .
   Web of Science ®Google Scholar