Some radii associated with polyharmonic equations
نویسندگان
چکیده
منابع مشابه
Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
when ε ≥ 0 is small. In particular, ∆2v + εv ≥ 0 in Ω, with v = ∆v = 0 on ∂Ω, implies v ≥ 0 for ε small. In numerical experiments ([14]) for one dimension a similar behaviour was observed under Dirichlet boundary conditions v = ∂ ∂nv = 0. In this paper we will derive a 3-G type theorem as in (1) but with G1,n replaced by the Green function Gm,n for the m-polyharmonic operator with Dirichlet bou...
متن کاملSome Second-order Partial Differential Equations Associated with Lie Groups
In this note we survey results in recent research papers on the use of Lie groups in the study of partial differential equations. The focus will be on parabolic equations, and we will show how the problems at hand have solutions that seem natural in the context of Lie groups. The research is joint with D.W. Robinson, as well as other researchers who are listed in the references.
متن کاملGlobal Optimal Regularity for the Parabolic Polyharmonic Equations
Regularity theory in PDE plays an important role in the development of second-order elliptic and parabolic equations. Classical regularity estimates for elliptic and parabolic equations consist of Schauder estimates, L estimates, De Giorgi-Nash estimates, KrylovSafonov estimates, and so on. L and Schauder estimates, which play important roles in the theory of partial differential equations, are...
متن کاملExistence of Nontrivial Solutions to Polyharmonic Equations with Subcritical and Critical Exponential Growth
The main purpose of this paper is to establish the existence of nontrivial solutions to semilinear polyharmonic equations with exponential growth at the subcritical or critical level. This growth condition is motivated by the Adams inequality [1] of Moser-Trudinger type. More precisely, we consider the semilinear elliptic equation (−∆) u = f(x, u), subject to the Dirichlet boundary condition u ...
متن کاملPolyharmonic homogenization, rough polyharmonic splines and sparse super-localization
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough (L∞) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interp...
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: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1971
ISSN: 0386-2194
DOI: 10.3792/pja/1195520109