## Boundary value problems of mathematical physics and related aspects of function theory, Part 4 |

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### Contents

An Example of Nonuniqueness Vanishing at Infinity of the Bounded Classical Solutions | 1 |

Interior Estimates of the First Derivatives of the Solutions of Quasilinear Nonuniformly | 9 |

BoundaryValue Problem for Degenerate SecondOrder Linear Parabolic Equations | 22 |

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analogous assume assumptions boundary conditions boundary-value problems bounded bounded function Cauchy inequality Cauchy problem Chapt classes of nonuniformly coefficients of Eq conditions 0.12 Consequently constant continued fraction convergence deduce defined degree of nonuniformity denote depending derivatives difference schemes Dirichlet problem domain Q elliptic and nonuniformly equal to zero estimate Euclidean space finite following conditions function Holder inequality homogeneous functions Inasmuch indices integral investigate latter left-hand side Lemma Let the coefficients linear hull matrix mean curvature Moscow Navier-Stokes equations nodes nonlinear nonuniformly elliptic equations nonuniformly parabolic equations norm notation O. A. and Ural'tseva operator order terms partition of unity points of Q polynomial prion proof of Theorem quasi-linear elliptic equations right-hand side satisfy conditions satisfy the conditions satisfy the following smooth smooth functions Solonnikov solution of problem solvability space Steklov sufficiently small Theorem 2.1 transformation uniformly variables vector