Dirichlet forms and semilinear elliptic equations with measure data
By Tomasz Klimsiak, A. Rozkosz. 2012
61 citations recorded by the source corpus.
We propose a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal) operators associated with regular Dirichlet forms and with measure data. Using the theory of backward stochastic differential equations we prove the existence and uniqueness of solutions in the case where the right-hand side of the equation is monotone and satisfies mild integrability assumption, and the measure is smooth. We also study regularity of solutions under the assumption that the measure is smooth and has finite total variation. Some applications of our general results are given.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/6ccd7c96f259c5c6f4173fc53e9afb1c714896e9
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In Applied Mathematics
- Tuomo Kuusi
- Giuseppe Mingione
- Yannick Sire
- Cristiana De Filippis
- Giampiero Palatucci
- Thomas Kruse
- Alexandre Popier
- Matteo Cozzi
In Computational Theory and Mathematics
- Tuomo Kuusi
- Giuseppe Mingione
- Yannick Sire
- Tomasz Klimsiak
- Frank Duzaar
- Paolo Baroni
- Cristiana De Filippis
- Verena Bogelein
In Finance
Citations in the corpus
- BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration (2014, background): “Proof: The proof follows closely the arguments in [21] and [29] (see also [6] or [40] for the Lipschitz case).”
- Nonlocal Equations with Measure Data (2014, background): “8) in the case s > 1/2 have been obtained in [29] and, in a different setting in [34].”
- Reflected BSDEs on filtered probability spaces (2014, methodology): “It is well suited for studying by probabilistic methods partial differential equations with irregular data (see [13, 14]).”