Shakhmurov, Veli2024-05-252024-05-2520131687-181210.1186/1687-1812-2013-422-s2.0-84877028347https://doi.org/10.1186/1687-1812-2013-42https://hdl.handle.net/20.500.14517/799In this paper, maximal regularity properties for linear and nonlinear high-order elliptic differential-operator equations with VMO coefficients are studied. For the linear case, the uniform coercivity property of parameter-dependent boundary value problems is obtained in spaces. Then, the existence and uniqueness of a strong solution of the boundary value problem for a high-order nonlinear equation are established. In application, the maximal regularity properties of the anisotropic elliptic equation and the system of equations with VMO coefficients are derived.eninfo:eu-repo/semantics/openAccessdifferential equations with VMO coefficientsboundary value problemsdifferential-operator equationsmaximal L-p regularityabstract function spacesnonlinear elliptic equationsArticleQ3WOS:0003167479000010