On the natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva
Study of global solutions of parabolic equations via a priori estimates III. Equations of p-Laplacian type
Time-periodic solutions of quasilinear parabolic differential equations II. Oblique derivative boundary conditions
We study boundary value problems for quasilinear parabolic equations when the initial condition is replaced by periodicity in the time variable. Our approach is to relate the theory of such problems to the classical theory for initial-boundary value problems. In the process, we generalize many previously known results.
Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.
Regularity of solutions of nonlinear elliptic boundary value problems.
Orlicz spaces, α-decreasing functions, and the Δ₂ condition
We prove some quantitatively sharp estimates concerning the Δ₂ and ∇₂ conditions for functions which generalize known ones. The sharp forms arise in the connection between Orlicz space theory and the theory of elliptic partial differential equations.
Higher regularity for nonlinear oblique derivative problems in Lipschitz domains
There is a long history of studying nonlinear boundary value problems for elliptic differential equations in a domain with sufficiently smooth boundary. In this paper, we show that the gradient of the solution of such a problem is continuous when a directional derivative is prescribed on the boundary of a Lipschitz domain for a large class of nonlinear equations under weak conditions on the data of the problem. The class of equations includes linear equations with fairly rough coefficients as well...
Gradient estimates for a new class of degenerate elliptic and parabolic equations
The first initial-boundary value problem for quasilinear second order parabolic equations
On the regularity of the minimizer of a functional with exponential growth
Minimizers of a functional with exponential growth are shown to be smooth. The techniques developed for power growth are not applicable to the exponential case.
Nonuniqueness for some linear oblique derivative problems for elliptic equations
It is well-known that the “standard” oblique derivative problem, in , on ( is the unit inner normal) has a unique solution even when the boundary condition is not assumed to hold on the entire boundary. When the boundary condition is modified to satisfy an obliqueness condition, the behavior at a single boundary point can change the uniqueness result. We give two simple examples to demonstrate what can happen.
The maximum principle for equations with composite coefficients.
Interior gradient estimates for nonuniformly parabolic equations. II.
Quenching of solutions of parabolic equations with nonlinear boundary conditions in several dimensions.
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