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On optimal $ L^1 $-control in coefficients for quasi-linear Dirichlet boundary value problems with $ BMO $-anisotropic $ p $-Laplacian

  • * Corresponding author: Gabriella Zecca

    * Corresponding author: Gabriella Zecca
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  • We study an optimal control problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principal part and $ L^1 $-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.

    Mathematics Subject Classification: Primary: 49J20; Secondary: 35J95.


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