Relationship between Laplacian Operator and D'alembertian Operator
نویسندگان
چکیده
Laplacian and D’Alembertian operators on functions are very important tools for several branches of Mathematics and Physics. In addition to their relevance, both operators are very used in vector calculus. In this paper, we show a relationship between the Laplacian and the D’Alembertian operators, not only on functions but also on vector fields defined on hypersurfaces in the m-dimensional Lorentzian spaces. We also define the B k1,...,kl m -product and Bm-congruence.
منابع مشابه
Infinitely Many Solutions for a Steklov Problem Involving the p(x)-Laplacian Operator
By using variational methods and critical point theory for smooth functionals defined on a reflexive Banach space, we establish the existence of infinitely many weak solutions for a Steklov problem involving the p(x)-Laplacian depending on two parameters. We also give some corollaries and applicable examples to illustrate the obtained result../files/site1/files/42/4Abstract.pdf
متن کاملInverse nodal problem for p-Laplacian with two potential functions
In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...
متن کاملDispersion relations and wave operators in self-similar quasicontinuous linear chains.
We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-similarity as a symmetry property requires the introduction of nonlocal particle-particle interactions. We derive a self-similar linear wave operator describing the dynamics of a quasicontinuous linear chain of infinite ...
متن کاملExistence and uniqueness of solutions for p-laplacian fractional order boundary value problems
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
متن کاملBilinear Fourier integral operator and its boundedness
We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.
متن کامل