BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS

Abstract

This paper considers elliptic equations of the form (*)and parabolic equations of the form (**)where and are positive homogeneous functions of the first order of homogeneity with respect to , convex upwards with respect and satisfying a uniform condition of strict ellipticity. Under certain smoothness conditions on and boundedness from above of the second derivatives of with respect to , solvability is established for these equations of a problem over the whole space, of the Dirichlet problem in a domain with a sufficiently regular boundary (for the equation (*)), and of the Cauchy problem and the first boundary value problem (for equation (**)). Solutions are sought in the classes , and their existence is proved with the aid of internal a priori estimates in . Bibliography: 29 titles.