Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts.

Florística e fitossociologia do componente arbóreo da transição Floresta Ombrófila Densa das Terras Baixas - Floresta Ombrófila Densa Submontana do Núcleo Picinguaba/PESM, Ubatuba, sudeste do Brasil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Modelagem das exigências de lisina para aves de postura em crescimento

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Jornal da UNESP, 2015, ano XXXI, n. 312

Jornal elaborado pela Assessoria de Comunicação e Imprensa da Reitoria da UNESP

Defining Regulatory Objectives for Contemporary Electronic Communications : Between a Rock and a Hard Place

Goal evaluation is an essential element of the process of designing regulatory frameworks. Lawyers and legal scholars do however tend to ignore it. The present paper stresses the importance of pinpointing the precise regulatory objectives in the fluid environment of electronic communications, since, due to their technological and economic development, they have become the vital basis for communication and distribution of information in modern societies. The paper attempts an analysis of the underlying regulatory objectives in contemporary communications and seeks to put together the complex puzzle of economic and societal issues.

Ms. hebr. oct. 274 - Aufzeichnungen über Ausgaben und Einnahmen bei der Verheiratung von Töchtern

Vorbesitzer: N.d.Bn.A.v.Rothschild (?); Freiherrlich Carl von Rothschildsche öffentliche Bibliothek