A series of problems in mechanics and physics are governed by theordinary Poisson equation which demands linearity,isotropy,and material homo-geneity.In this paper a generalization with respect to nonlinearity,anisotropy,andinhomogeneity is made.Starting from the canonical basic equations in the primal anddual formulation respectively we derive systematically the corresponding generalizedvariational principles;under certain conditions they can be extended to so calledcomplementary extremum principles allowing for global bounds.For simplicity arestriction to two dimensional problems is made,including twice-connected domains.
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