Boundary Value Problems of Mathematical Physics and Related Aspects of Function Theory, Part 4Valeriĭ Pavlovich Ilʹin |
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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A₁ analogous assume assumptions boundary-value problem bounded C₁ C₂ Cauchy inequality Cauchy problem Chapt coefficients of Eq conditions 0.12 const constant continued fraction convergence denote depending derivatives differentiable Dirichlet problem domain dx dt dxdt estimate max estimate of max Euclidean space finite following inequality function u(x,t Hölder Hölder continuity Hölder inequality homogeneous functions Inasmuch integral L₂ Lemma Let the coefficients Linear and Quasi-linear Mathematical matrix mean curvature Navier-Stokes equations nonlinear nonuniformly elliptic equations norm O. A. and Ural'tseva obtain operator P₁ P₂ parabolic equations points priori estimates proof of Theorem Q₁ quasi-linear elliptic equations quasi-linear parabolic equations right-hand side satisfy conditions satisfy the conditions satisfy the following Solonnikov solution of problem solvability space Steklov Theorem 3.1 transformation U₁ U₂ uniformly V₁ V₂ vector W₂ ди