Giovanni Franzina, Pier Domenico Lamberti
Abstract:
We consider the Dirichlet eigenvalue problem
where the unknowns
(the eigenfunction)
and
(the eigenvalue),
is an arbitrary
domain in
with finite measure,
,
,
if
and
if
.
We study several existence and uniqueness results as well as
some properties of the solutions. Moreover, we indicate how to
extend to the general case some proofs known in the classical
case
.
Submitted January 14, 2010. Published February 16, 2010.
Math Subject Classifications: 35P30.
Key Words: p-laplacian; eigenvalues; existence; uniqueness results
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Giovanni Franzina Dipartimento di Matematica, University of Trento Trento, Italy email: g.franzina@email.unitn.it | |
Pier Domenico Lamberti Dipartimento di Matematica Pura e Applicata University of Padova, Padova, Italy email: lamberti@math.unipd.it |
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