Nonlinear elliptic-parabolic equations and B-pseudomonotonicity

Elliptic and Parabolic Equations

Elliptic equations: 1. Harmonic functions 2. Perron’s method 3. Potential theory 4. Existence results; the method of suband supersolutions 5. Classical maximum principles for elliptic equations 6. More regularity, Schauder’s theory for general elliptic operators 7. The weak solution approach in one space dimension 8. Eigenfunctions for the Sturm-Liouville problem 9. Generalization to more dimen...

Nonlinear Elliptic and Parabolic Equations with Fractional Diffusion

A pseudo - monotonicity adapted to doubly nonlinear elliptic - parabolic equations

Pseudo-monotonicity seems to be a good notion to deal with convergence in non-linear terms of partial differential equations. J.-L. Lions [16] used two different definitions of pseudo-monotonicity for elliptic and parabolic problems, and derived associated existence results. Nonlinear elliptic-parabolic equations are intermediate equations for which an intermediate pseudo-monotonicity is define...

Elliptic and Parabolic Equations with Nonstandard Nonlinearity

• Mikhail Surnachev, Keldish Institute of Applied Mathematics Moscow Parabolic Equations Degenerating on a Part of the Domain ABSTRACT. In this work we study nonlinear parabolic equations of the p-Laplace type degenerating on a part of the domain. The degeneration is controlled by a small parameter. For the fixed value of this parameter, the results we discuss fall within the scope of E. DiBene...

Parabolic and Elliptic Equations with Vmo Coefficients

An Lp-theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class V MOx, which, in particular, contains all functions independent of x. Weak uniqueness of the martingale problem associated with such equations is obtained.