Variable exponent spaces Free boundary problem 6 P (x)-Laplacian 6 Singular perturbation 6 Concentration-compactness principle 4 Elliptic equations 4 Free-boundary problems 4 H2 regularity 4 Inhomogeneous problem 4 Laplace transforms 4 Minimization 4 Optimization 4 Regularity of the free boundary 4 Variable exponents 4 Boundary value problems 2 Differentiable functions 2 Discontinuous Galerkin 2 Discontinuous Galerkin FEM 2 Discontinuous Galerkin methods 2 Discontinuous galerkin 2 Free boundaries 2 Free boundary 2 Galerkin methods 2 Harnack's inequality 2 Image processing 2 Lipschitz continuous 2 Lipschitz functions 2 Lipschitz regularity 2 Local bounds 2 Minimization problem 2