Linear and Quasi-linear Equations of Parabolic TypeAmerican Mathematical Soc., 1968 - 648 páginas In this volume boundary value problems are studied from two points of view; solvability, unique or otherwise, and the effect of various smoothness properties of the given functions on the smoothness of the solutions. There are seven chapters contained in this volume. Chapter One gives a statement of the new results and an historical sketch. Chapter two introduces the various function spaces typical of modern Russian-style functional analysis. Chapters three and four deal with linear equations. Chapter six concerns itself with quasilinear equations, and chapter seven with systems of equations. These last four chapters can be read independently of one another. |
Índice
Prefactory note to the Translation ix | 1 |
Nikolai V Ivanov Subgroups of Teichmüller modular groups 1992 | 35 |
Linear equations with discontinuous coefficients 133 | 46 |
Otras ediciones - Ver todo
Linear and Quasi-linear Equations of Parabolic Type Olʹga Aleksandrovna Ladyzhenskai︠a︡,Vsevolod Alekseevich Solonnikov,Nina Nikolaevna Uralʹt︠s︡eva No hay ninguna vista previa disponible - 1968 |
Términos y frases comunes
analogous arbitrary Banach space consisting belong boundary conditions boundary value problems bounded functions boundedness c₁ Cauchy problem Chapter classical solutions classical statement coefficients and free conditions 3.12 continuous derivatives continuous functions cylinder d/dx defined derivatives with respect differential equations domain elements elliptic equation 3.5 equations 2.1 equations of parabolic equations of second example existence finite free terms func function spaces function u(x Hilbert space Hölder condition Hölder continuous Hölder spaces inequality investigated known functions lateral surface linear and quasi-linear linear equations maximum principle method nonlinear nonnegative nonpositive parabolic equations parabolic type positive numbers problems for equations proof proved quasi-linear equations restrictions satisfying condition second order singularities smooth functions solution of problem solution u(x solutions of equations t)ux t₁ terms of max Theorem 2.1 tion uniformly parabolic unique solvability uniqueness theorems valid zero ατ ди