## Boundary value problems of mathematical physics and related aspects of function theory, Volume 2 |

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### Contents

Estimates of Convolution Operators | 1 |

Local Maximal Estimates of the Modulus of the First Derivatives of the Solutions | 37 |

Modifications of the NavierStokes Equations for Large Velocity Gradients | 57 |

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Akad analogous arbitrary assume ball boundary-value problem bounded function boundedness Cauchy inequality Cauchy problem Chapt class of functions coefficients components condition 0.3 convergence convolution operator cutoff function deduce denote derivatives differential equations Dirichlet problem elliptic equations equal to zero estimated in terms finite following estimate holds following inequality holds following theorem Fourier series Fourier transform func Holder Holder inequality Inasmuch inequalities 2.9 Inst integral identity investigate K. K. Golovkin kernel left-hand side Lemma linear set matrix monotonic Moscow multi-index multipliers N. N. Ural'tseva Nauk SSSR Navier-Stokes equations nonuniformly-elliptic equations O. A. Ladyzhenskaya obtain operator 54 ordinary differential equations parabolic equations properties proved the following quasilinear quasilinear elliptic right-hand side satisfies condition satisfying the condition set of numbers smoothness solution of problem space Steklov Mathematical Institute subdomain sufficiently large tion Trudy Mat unique solvability V. A. Solonnikov valid variables verified virtue