Everywhere H¨older Continuity of Solutions of Certain Degenerate Elliptic Systems

Consider on G a degenerate elliptic system in diagonal form of which solutions are in a weighted Sobolev space with weight function that belongs to the Muckenhoupt class A2 and characteristic values of the leading coefficient matrix that are proportional to a positive power of the modulus of the unknown solution. The everywhere H¨older continuity in the interior of G is proved to bounded solutions