| Elliptic partial differential equation is one of the important types of partial differential equations,it has important applications in physics,chemistry,engineering and other disciplines.This thesis is devoted to the Calderón-Zygmund type regularity estimates for weak solutions of elliptic equations.First,the global BMO estimates for weak solutions inR~n are obtained under the natural growth conditions.Then,the more general elliptic equations are considered,the global BMO estimates for weak solutions in R~n are studied under BMO conditions and natural growth conditions.Finally,the global Lorentz estimates for weak solutions of elliptic equations with BMO coefficients are studied on convex domains.The full text is divided into five chapters as follows:In Chapter 1,the research background and the recent development involving our research topic at home and abroad are recalled.In Chapter 2,the symbols,definitions and famous lemmas are introduced.In Chapter 3,the nonlinear elliptic equations with H(?)lder continuous coefficients are studied under natural growth conditions.The global BMO estimates for weak solutions inR~n are obtained by using perturbation discussion,John-Nirenberg inequality,Hardy-Littlewood maximum function theory and Giaquinta-Giusti iterative lemma.In Chapter 4,the more general elliptic equations are considered.The methods of dealing with discontinuous coefficients are used in the perturbation discussion,the global BMO estimates for weak solutions inR~n are obtained under the small BMO conditions and natural growth conditions.In Chapter 5,the Calderón-Zygmund type estimates for weak solutions of elliptic equations with BMO coefficients are studied.The methods of dealing with discontinuous coefficients are applied to bounded convex domains,the global Lorentz estimates for weak solutions are obtained on convex domains by the approximation principle,Hardy-Littlewood maximum function theory,compactness method and Vitali covering lemma.Figure 0;Table 0;Reference 61... |
