TECHNOLOGY FOCUS - ELECTRICAL POWER AND ENERGY - Preferred Component: At least one of the anode, the electrolyte and the cathode is deposited on the reformer slab by plasma spraying. The reformer-supported solid oxide fuel cell further comprises bipolar plate(s). The reformer slab is contiguous to one of the bipolar plates. The electroconductive mixture is pressed, cast, thermally sprayed, extruded or shaped formed by thermal spraying into the reformer slab. The anode comprises a mixture of a second electrolyte and a metal catalyst. The electrolyte comprises a doped ceramic ionic conductor. The solid oxide fuel cell is operated at 500-700degreesC. The reformer slab has waves on surface(s) of the slab and a flat surface at least partially surrounding the grooved surface of the slab. It is provided with successive layers of an anode material, an electrolyte material, and a cathode material on the waved surface to constitute the solid oxide fuel cell. Only the electrolyte material covers the fiat surface. The reformer slab is sintered in a reducing atmosphere. It is deposited on the bipolar plate. Preferred Property: The thickness of the reformer slab is 1-5 mm. The thickness of the anode, the electrolyte and the cathode is 5-100 mum. Preferred Method: The method further comprises pressing, casting, thermal spraying, extruding, or shaped forming by thermal spraying the mixture into the slab having a thickness of 1-5 mm; sintering the slab in the reducing atmosphere; spraying the anode material over the slab until the anode material thickness of 5-100 mum is reached; spraying the electrolyte material over the anode material until the electrolyte material thickness of 5-100 mum is reached; spraying the cathode material over the electrolyte material until a cathode material thickness of 5-100 mum is reached; firing the assembly of the reformer slab, the anode, the electrolyte, and the cathode; and depositing the reformer slab onto the bipolar plate. The combination of the reformer slab, the anode, the electrolyte, and the cathode forms an individual cell. The individual cells are stacked into a supporting structure.    TECHNOLOGY FOCUS - CERAMICS AND GLASS - Preferred Component: The electroconductive mixture comprises the polymeric ceramic material (up to 30 wt.%). INORGANIC CHEMISTRY - Preferred Material: The cathode comprises a perovskite material from LSM, LSF or LSCF.