The Minty-Browder theorem for nonlinear elliptic equations involving p-Laplacian with singular coefficients under form boundary conditions

Abstract. We consider the elliptic parabolic partial differential equation with singular coefficients under the rather general form boundary conditions. We proved that the bounded operator associated with the elliptic equation satisfies monotony, coercivity, and semicontinuity conditions. Employing Minty-Browder arguments, we establish the existence and uniqueness of the weak solution to the elliptic equation with singular coefficients under form-boundary conditions.