We study an optimal control problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principal part and L1-control in coefficient of the low-order term. We assume that the matrix of anisotropy belongs to BMO-space. Since we cannot expect to have a solution of the state equation in the classical Sobolev space, we introduce a suitable functional class in which we look for solutions and prove existence of optimal pairs using an approximation procedure and compactness arguments in variable spaces.
On Optimal L1-Control in Coefficients for Quasi-Linear Dirichlet Boundary Value Problems with BMO-Anisotropic p-Laplacian / De Maio, U.; Kogut, P. I.; Zecca, G.. - In: MATHEMATICAL CONTROL AND RELATED FIELDS. - ISSN 2156-8472. - 10:4(2020), pp. 827-854. [10.3934/mcrf.2020021]
On Optimal L1-Control in Coefficients for Quasi-Linear Dirichlet Boundary Value Problems with BMO-Anisotropic p-Laplacian
De Maio U.;Zecca G.
2020
Abstract
We study an optimal control problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principal part and L1-control in coefficient of the low-order term. We assume that the matrix of anisotropy belongs to BMO-space. Since we cannot expect to have a solution of the state equation in the classical Sobolev space, we introduce a suitable functional class in which we look for solutions and prove existence of optimal pairs using an approximation procedure and compactness arguments in variable spaces.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
