On quasilinear Beltrami-type equations with degeneration
نویسندگان
چکیده
منابع مشابه
On Planar Beltrami Equations and Hölder Regularity
We provide estimates for the Hölder exponent of solutions to the Beltrami equation ∂f = μ∂f + ν∂f , where the Beltrami coefficients μ, ν satisfy ‖|μ|+ |ν|‖∞ < 1 and =(ν) = 0. Our estimates depend on the arguments of the Beltrami coefficients as well as on their moduli. Furthermore, we exhibit a class of mappings of the “angular stretching” type, on which our estimates are actually attained.
متن کاملOn Beltrami equations and Hölder regularity
We estimate the Hölder exponent α of solutions to the Beltrami equation ∂f = μ∂f , where the Beltrami coefficient satisfies ‖μ‖∞ < 1. Our estimate improves the classical estimate α ≥ ‖Kμ‖ , where Kμ = (1 + |μ|)/(1 − |μ|), and it is sharp, in the sense that it is actually attained in a class of mappings which generalize the radial stretchings. Some other properties of such mappings are also prov...
متن کاملOn Quasilinear Elliptic Equations in Ir
In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −∆u = h(x)u in IR , where 0 < q < 1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.
متن کاملQuasilinear and Hessian Equations of Lane–emden Type
The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane–Emden type, including the following two model problems: −∆pu = u + μ, Fk[−u] = u + μ, u ≥ 0, on R, or on a bounded domain Ω ⊂ R. Here ∆p is the pLaplacian defined by ∆pu = div (∇u|∇u|p−2), and Fk[u] is the k-Hessian defined as the sum of k× k principal minors o...
متن کاملAnisotropic quasilinear elliptic equations with variable exponent
We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory. 2000 Mathematics Subject Classification: 35J60, 35J62, 35J70.
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: Mathematical Notes
سال: 2011
ISSN: 0001-4346,1573-8876
DOI: 10.1134/s0001434611090112