Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations
نویسندگان
چکیده
منابع مشابه
Hyperbolic Partial Differential Equations and Geometric Optics
§1.1. The method of characteristics §1.2. Examples of propagation of singularities using progressing waves §1.3. Group velocity and the method of nonstationary phase §1.4. Fourier synthesis and rectilinear propagation §1.5. A cautionary example in geometric optics §1.6. The law of reflection §1.6.1. The method of images §1.6.2. The plane wave derivation §1.6.3. Reflected high frequency wave pac...
متن کاملAnd Pointwise Estimates for a Class of Degenerate Elliptic Equations
In this paper we prove a Sobolev-Poincaré inequality for a class of function spaces associated with some degenerate elliptic equations. These estimates provide us with the basic tool to prove an invariant Harnack inequality for weak positive solutions. In addition, Holder regularity of the weak solutions follows in a standard way. 1 Let Sf = YJl ,=i 9j(ajjdj) be a second-order degenerate ellipt...
متن کاملPointwise Estimates of Solutions to Semilinear Elliptic Equations and Inequalities
We obtain sharp pointwise estimates for positive solutions to the equation −Lu+V u = f , where L is an elliptic operator in divergence form, q ∈ R\{0}, f ≥ 0 and V is a function that may change sign, in a domain Ω in R, or in a weighted Riemannian manifold.
متن کاملSemigroups and Evolution Equations: Functional Calculus, Regularity and Kernel Estimates
This is a survey on recent developments of the theory of one-parameter semigroups and evolution equations with special emphasis on functional calculus and kernel estimates. Also other topics as asymptotic behavior for large time and holomorphic semigroups are discussed. As main application we consider elliptic operators with various boundary conditions. Semigroups and evolution equations: Funct...
متن کاملSupercritical geometric optics for nonlinear Schrodinger equations
We consider the small time semi-classical limit for nonlinear Schrödinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To overcome this issue, we introduce new unknown functions, which are defined nonlinearly in terms of the wave function itself. This approach provides a local vers...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2017
ISSN: 0010-3640
DOI: 10.1002/cpa.21691