Regularity up to the boundary for some degenerate elliptic operators

References

• Di Fazio G. Dirichlet problem characterization of regularity. Manuscripta Math. 1994;84:47–56.
   Web of Science ®Google Scholar
• Vitanza C, Zamboni P. Necessary and sufficient conditions for Holder continuity of solutions of degenerate Schrödinger operators. Le Matematiche. 1997;52(2):393–409.
   Google Scholar
• Aizenman M, Simon B. Brownian motion and Harnack's inequality for Schrödinger operators. Comm Pure Appl Math. 1982;35:209–271.
   Web of Science ®Google Scholar
• Chiarenza F, Fabes E, Garofalo N. Harnack's inequality for Schrodinger operators and the continuity of solutions. Proc Amer Math Soc. 1986;98(3):415–425.
   Web of Science ®Google Scholar
• Simader CG. An elementary proof of Harnack's inequality for Schrodinger operators and related topics. Math Z. 1990;203(1):129–152.
   Web of Science ®Google Scholar
• Di Fazio G. Hölder-continuity of solutions for some Schrodinger equations. Rend Sem Mat Univ Padova. 1988;79:173–183.
   Google Scholar
• Di Fazio G. Poisson equation in Morrey spaces. J Math Anal Appl. 1992;163:157–167.
   Web of Science ®Google Scholar
• Kurata K. Continuity and Harnack's inequality for solutions of elliptic partial differential equations of second order. Indiana Univ Math J. 1994;43(2):411–440.
   Web of Science ®Google Scholar
• Trudinger NS. On Harnack type inequalities and their application to quasilinear elliptic equations. Comm Pure Appl Math. 1967;20:721–747.
   Web of Science ®Google Scholar
• Rakotoson JM, Ziemer WP. Local behavior of solutions of quasilinear elliptic equations with general structure. Trans Amer Math Soc. 1990;319(2):747–764.
   Web of Science ®Google Scholar
• Di Fazio G, Fanciullo MS, Zamboni P. Harnack inequality and regularity for degenerate quasilinear elliptic equations. Math Z. 2010;264(3):679–695.
   Web of Science ®Google Scholar
• Di Fazio G, Zamboni P. Regularity for quasilinear degenerate elliptic equations. Math Z. 2006;253(4):787–803.
   Web of Science ®Google Scholar
• Zamboni P. The Harnack inequality for quasilinear elliptic equations under minimal assumptions. Manuscripta Math. 2000;102(3):311–323.
   Web of Science ®Google Scholar
• Zamboni P. Local boundedness of solutions of quasilinear elliptic equations with coefficients in Morrey spaces. Boll Unione Mat Ital B. 1994;8(4):985–997.
   Google Scholar
• Zamboni P. Local behavior of solutions of quasilinear elliptic equations with coefficients in Morrey spaces. Rend Mat Appl. 1995;15(2):251–262.
   Google Scholar
• Di Fazio G, Fanciullo MS, Zamboni P. Harnack inequality and continuity of weak solutions for doubly degenerate elliptic equations. Math Z. 2019;292:1325–1336.
   Web of Science ®Google Scholar
• Gutierrez CE. Harnack's inequality for degenerate Schrodinger operators. Trans AMS. 1989;312:403–419.
   Web of Science ®Google Scholar
• Fabes E, Kenig C, Serapioni R. The local regularity of solutions of degenerate elliptic equations. Comm Partial Differ Eq. 1982;7(1):77–116.
   Web of Science ®Google Scholar
• Zamboni P. Hölder continuity for solutions of linear degenerate elliptic equations under minimal assumptions. J Differ Eq. 2002;182(1):121–140.
   Web of Science ®Google Scholar
• Di Fazio G, Fanciullo MS, Zamboni P. Harnack inequality and smoothness for quasilinear degenerate elliptic equations. J Differ. Equations. 2008;245(10):2939–2957.
   Web of Science ®Google Scholar
• Mohammed A. Hölder continuity of solutions of some degenerate elliptic differential equations. Bull Austral Math Soc. 2000;62:369–377.
   Web of Science ®Google Scholar
• Citti G, Garofalo N, Lanconelli E. Harnack's inequality for sum of squares of vector fields plus a potential. Amer J Math. 1994;115:699–734.
   Web of Science ®Google Scholar
• Citti G, Di Fazio G. Hölder continuity of the solutions for operators which are a sum of squares of vector fields plus a potential. Proc Amer Math Soc. 1994;122:741–750.
   Web of Science ®Google Scholar
• Di Fazio G, Zamboni P. Hölder continuity for quasilinear subelliptic equations in Carnot Carathéodory spaces. Math Nachr. 2004;272:3–10.
   Web of Science ®Google Scholar
• Di Fazio G, Zamboni P. Local regularity of solutions to quasilinear subelliptic equations in Carnot Carathéodory spaces. Boll Unione Mat Ital B. 2006;29(2):485–504.
   Google Scholar
• Lu G. On Harnack's inequality for a class of strongly degenerate Schrödinger operators formed by vector fields. Differ Int Eq. 1994;7(1):73–100.
   Google Scholar
• Di Fazio G, Fanciullo MS, Zamboni P. Harnack inequality for a class of strongly degenerate elliptic operators formed by Hörmander vector fields. Manuscripta Math. 2011;135(3–4):361–380.
   Web of Science ®Google Scholar
• Di Fazio G, Fanciullo MS, Zamboni P. Regularity for a class of strongly degenerate quasilinear operators. J Differ Eq. 2013;255(11):3920–3939.
   Web of Science ®Google Scholar
• Di Fazio G, Fanciullo MS, Zamboni P. Harnack inequality for degenerate elliptic equations and sum operators. Comm Pure Appl Anal. 2015;14(6):2363–2376.
   Web of Science ®Google Scholar
• Di Fazio G, Fanciullo MS, Zamboni P. Local regularity for strongly degenerate elliptic equations and weighted sum operators. Differ Int Eq. July/August 2019;32(7-8):479–492.
   Web of Science ®Google Scholar
• Serrin J. Local behaviour of solutions of quasilinear equations. Acta Math. 1964;111:247–302.
   Web of Science ®Google Scholar
• Nagel A, Stein EM, Wainger S. Balls and metrics defined by vector fields. I. basic properties. Acta Math. 1985;155(1–2):103–147.
   Web of Science ®Google Scholar
• Calderon AP. Inequalities for the maximal function relative to a metric. Studia Math. 1976;57(3):297–306.
   Web of Science ®Google Scholar
• Lu G. Weighted Poincaré and Sobolev inequality for vector fields satisfying Hörmander's condition and its application. Rev Iberoamericana. 1992;8(3):367–439.
   Google Scholar
• Ragusa MA, Zamboni P. Local regularity of solutions to quasilinear elliptic equations with general structure. Commun Appl Anal. 1999;3(1):131–147.
   Google Scholar
• Di Fazio G, Fanciullo MS, Zamboni P. Harnack inequality and smoothness for some non linear degenerate elliptic equations. Minimax Theory Appl, Conf “Nonlinear Phenomena: Theory Appl”. 2019;4(1):87–99.
   Google Scholar
• Buckley SM. Inequalities of John-Nirenberg type in doubling spaces. J Anal Math. 1999;79:215–240.
   Web of Science ®Google Scholar