## 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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A,QT analogous assume assumptions boundary-value problem bounded domain bounded function Cauchy inequality Cauchy problem Chapt class Wt classes of nonuniformly coefficients of Eq conditions 0.12 Consequently constant continued fraction convergence deduce defined denote depending derivatives difference schemes Dirichlet problem dxdt elliptic and nonuniformly equal to zero Euclidean space finite following conditions function Holder inequality homogeneous functions Inasmuch integral investigate left-hand side Lemma Let the coefficients Linear and Quasi-linear linear hull matrix mean curvature Navier-Stokes equations nodes nonlinear nonuniformly elliptic equations nonuniformly parabolic equations norm notation O. A. and Ural'tseva O. A. Ladyzhenskaya operator partition of unity points polynomial priori estimates problem for quasi-linear proof of Theorem quasi-linear elliptic equations quasi-linear parabolic equations right-hand side satisfy conditions satisfy the conditions satisfy the following smooth Solonnikov solution of problem space Steklov sufficiently large sufficiently small Theorem 2.1 transformation uniformly vector