TY - JOUR

T1 - Boundedly nonhomogeneous elliptic and parabolic equations

AU - Krylov, N. V.

PY - 1983/6/30

Y1 - 1983/6/30

N2 - 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.

AB - 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.

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U2 - 10.1070/IM1983v020n03ABEH001360

DO - 10.1070/IM1983v020n03ABEH001360

M3 - Article

AN - SCOPUS:84878313116

SN - 0025-5726

VL - 20

SP - 459

EP - 492

JO - Mathematics of the USSR - Izvestija

JF - Mathematics of the USSR - Izvestija

IS - 3

ER -