Search results for " Elliptic"

Indefinite integrals involving the Jacobi Zeta and Heuman Lambda functions

2017

ABSTRACTJacobian elliptic functions are used to obtain formulas for deriving indefinite integrals for the Jacobi Zeta function and Heuman's Lambda function. Only sample results are presented, mostly obtained from powers of the twelve Glaisher elliptic functions. However, this sample includes all such integrals in the literature, together with many new integrals. The method used is based on the differential equations obeyed by these functions when the independent variable is the argument u of elliptic function theory. The same method was used recently, in a companion paper, to derive similar integrals for the three canonical incomplete elliptic integrals.

Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions

2021

Abstract We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.

Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources

2018

In this paper we construct a viscosity solution of a two-phase free boundary problem for a class of fully nonlinear equation with distributed sources, via an adaptation of the Perron method. Our results extend those in [Caffarelli, 1988], [Wang, 2003] for the homogeneous case, and of [De Silva, Ferrari, Salsa, 2015] for divergence form operators with right hand side.

On the number of prime divisors of the order of elliptic curves modulo p

2005

Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential

2016

Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations

Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential

2016

Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations −Δpu − μ |x| p |u| p−2 u + m|u| p−2 u = f(u), x ∈ RN , where 1 0 and f is a continuous function. peerReviewed

Variational differential inclusions without ellipticity condition

2020

The paper sets forth a new type of variational problem without any ellipticity or monotonicity condition. A prototype is a differential inclusion whose driving operator is the competing weighted $(p,q)$-Laplacian $-\Delta_p u+\mu\Delta_q u$ with $\mu\in \mathbb{R}$. Local and nonlocal boundary value problems fitting into this nonstandard setting are examined.

A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence

2016

The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.

Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term

2021

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.

An automated image analysis methodology for classifying megakaryocytes in chronic myeloproliferative disorders

2008

This work describes an automatic method for discrimination in microphotographs between normal and pathological human megakaryocytes and between two kinds of disorders of these cells. A segmentation procedure has been developed, mainly based on mathematical morphology and wavelet transform, to isolate the cells. The features of each megakaryocyte (e.g. area, perimeter and tortuosity of the cell and its nucleus, and shape complexity via elliptic Fourier transform) are used by a regression tree procedure applied twice: the first time to find the set of normal megakaryocytes and the second to distinguish between the pathologies. The output of our classifier has been compared to the interpretati…