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 A₁j analogous assume assumptions boundary-value problems C₁ C₂ Cauchy inequality Cauchy problem Chapt coefficients of Eq conditions 0.12 const constant continued fraction convergence denote depending derivatives differentiable Dirichlet problem dx dt dxdt elliptic and nonuniformly equal to zero estimate max estimate of max finite following inequality function u(x,t Hölder Hölder continuity Hölder inequality homogeneous functions Inasmuch integral L₂ Lemma Linear and Quasi-linear Mathematical matrix mean curvature Navier-Stokes equations nonlinear nonuniformly elliptic equations norm obtain operator P₁ parabolic equations points priori estimates proof of Theorem proved Q₁ quasi-linear elliptic equations quasi-linear parabolic equations right-hand side S₁ satisfy conditions satisfy the conditions satisfy the following Solonnikov solution of problem solvability space Theorem 2.1 transformation U₁ U₂ uniformly V₁ V₂ vector W₂ ди วน อน