The Laplacian with Robin Boundary Conditions involving signed measures

Author name not available (Why is that?)

Publication date: 5 February 2019

Abstract: In this work we propose to study the general Robin boundary value problem involving signed smooth measures on an arbitrary domain

O m e g a

of

m a t h b b R^{d}

. A Kato class of measures is defined to insure the closability of the associated form

(m e m, m f m)

. Moreover, the associated operator

D e l t a_{m u}

is a realization of the Laplacian on

L^{2} (O m e g a)

. In particular, when

| m u |

is locally infinite everywhere on

p o

,

D e l t a_{m u}

is the laplacian with Dirichlet boundary conditions. On the other hand, we will prove that he semigroup

(e m u)_{t g e q 0}

is sandwitched between

(e m u p)_{t g e q 0}

and

(e m u n)_{t g e q 0}

and we will see that the converse is also true.

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