ΜΙΑ ΠΙΘΑΝΟΘΕΩΡΗΤΙΚΗ ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΕΞΙΣΩΣΗΣ MONGE-AMPERE

THE SUBJECT WE ARE DEALING WITH CAN BE DIVIDED AS FOLLOWS: A) POSSIBILITY OF STOCHASTIC REPRESENTATION OF THE GENERALISED SOLUTION OF THE REAL MONGE-AMPERE EQUATION MU=F>0 K D, K=Φ ON ΘD, D C IRD OPEN-BOUNDED CONVEX. PARTLY IN PARALLEL TO THE WORK BY B. GAVEAN, WHO TREATED THE COMPLEX CASE, GENERAL RESULTS ARE OBTAINED. SPECIFICALLY THE SOLUTION CAN BE STOCHASTICALLY REPRESENTED IF O<F E L (D), Φ E C (ΘD), D C IRD STRICTLY CONVEX (ΘD NOT NECESSARILLY SMOOTH). PARTICULARLY IF Φ=0 A BARRIER CONDITION ON ΘD IS SUFFICIENT. IN THIS CONTEXT A SIMPLIFIEDPROOF OF KRYLER'S INEQUALITY IS OBTAINED. B) PROBABILISTIC DEMONSTRATION OF THE EXISTENCE OF THE SOLUTION OF THE MONGE- AMPERE EQUATION (IN THE GENERALISED SENSE) OPTIMAL STOCHASTIC CONTROL TECHNIQUES IN CONJUNCTION WITH A STOCHASTIC VERSION OF IDEAS DEVELOPED BY P.L. LIONS CAN ASSURE A PURELY PROBABILISTIC DEMONSTRATION OF EXISTENCE OF THE SOLUTION. THE METHOD AFTER MINOR CHANGES, CAN ALSO APPLY TO THE COMPLEX CASE. AN E-OPTIMAL CONTROL CAN BE REALISED FOR THE ASSOCIATED STOCHASTIC PROBLEM WHEN FE LP (D), P>D.

Grantor dc:publisher

National Technical University of Athens (NTUA)

Year dc:date

1988

Author dc:creator

• Σπηλιώτης, Ιωάννης

• ΑΝΙΣΟΤΗΤΑ ΚΡΥΛΟΒ
• ΓΕΝΙΚΕΥΜΕΝΗ ΛΥΣΗ
• ΕΞΙΣΩΣΗ ΜΟΝΖ-ΑΜΠΕΡ
• ΣΤΟΧΑΣΤΙΚΗ ΑΝΑΠΑΡΑΣΤΑΣΗ
• ΣΤΟΧΑΣΤΙΚΟΣ ΒΕΛΤΙΣΤΟΣ ΕΛΕΓΧΟΣ
• GENE LISED SOLUTION
• KRYLOV'S INEQUALITY
• MONGE-AMPERE EQUATION
• STOCHASTIC OPTIMAL CONTROL
• STOCHASTIC REPRESENTATION
• Φυσικές Επιστήμες
• Μαθηματικά
• Natural Sciences
• Mathematics

Language dc:language

gre

Identifier

10.12681/eadd/0700

OAI identifier oai:identifier

oai:10442/0700