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Displaying 61 –
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As written in L. Schwartz' book, Heaviside's theory of cables is an important source of the theory of generalized functions. The partial differential equations he discussed were the usual heat equation and the simplest hyperbolic equations of one space dimension, but he had to solve them as evolution equations in the unusual direction of the distance along which the electric signals propagate. Although he obtained explicit expressions of solutions, which were of great economical values, it has not...
BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor connection which yields an invariant prolongation of the first operator. The explicit calculation is presented in the case of conformal Killing forms.
Fundamental solutions to linear partial differential equations with constant coefficients are represented in the form of Laplace type integrals.
We consider an Hamilton-Jacobi equation of the formwhere is assumed Borel measurable and quasi-convex in . The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation (1) coupled with Dirichlet boundary conditions, and a stability result. The relation among Monge and Lipschitz subsolutions is also discussed.
We consider an Hamilton-Jacobi equation of the form
where H(x,p) is assumed Borel measurable and quasi-convex in
p. The notion of Monge solution, introduced by Newcomb and Su,
is adapted to this setting making use of suitable metric devices.
We establish the comparison principle for Monge sub and
supersolution, existence and uniqueness for equation ([see full text])
coupled with Dirichlet boundary conditions, and a stability result. The
relation among Monge and Lipschitz subsolutions is also...
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188