Semigroups, potential spaces and applications to (S)PDE

DOI10.1007/s11118-011-9238-9zbMath1251.60053OpenAlexW2117885730MaRDI QIDQ411539

Martina Zähle, Michael Hinz

Publication date: 4 April 2012

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-011-9238-9

zbMATH Keywords

potential theorySPDEmetric measure spacesnonlinear Cauchy problems

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) One-parameter semigroups and linear evolution equations (47D06) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Initial value problems for PDEs with pseudodifferential operators (35S10) Potential theory on fractals and metric spaces (31E05)

Related Items

Elementary Pathwise Methods for Nonlinear Parabolic and Transport Type Stochastic Partial Differential Equations with Fractal Noise ⋮ Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates ⋮ (S)PDE on Fractals and Gaussian Noise ⋮ Existence and space-time regularity for stochastic heat equations on p.c.f. fractals ⋮ Regularity of the solutions to SPDEs in metric measure spaces ⋮ On the viscous Burgers equation on metric graphs and fractals

Cites Work

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• The construction of Brownian motion on the Sierpinski carpet
• Young integrals and SPDEs
• A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps
• Generalized Bessel and Riesz potentials on metric measure spaces
• Gradient type noises. II: Systems of stochastic partial differential equations
• Semigroups of linear operators and applications to partial differential equations
• Hardy-Littlewood theory for semigroups
• Upper bounds for symmetric Markov transition functions
• Dirichlet forms and analysis on Wiener space
• Integration with respect to fractal functions and stochastic calculus. I
• Some Dirichlet spaces obtained by subordinate reflected diffusions
• Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E's
• Dirichlet forms and symmetric Markov processes
• Brownian motion on a random recursive Sierpinski gasket
• Evolution equations driven by a fractional Brownian motion
• Censored stable processes
• Stochastic evolution equations with fractional Brownian motion
• Harmonic analysis for resistance forms.
• Ultracontractivity and Nash type inequalities
• On the Dirichlet problem for pseudodifferential operators generating Feller semigroups
• A concise course on stochastic partial differential equations
• Integration with respect to Fractal Functions and Stochastic Calculus II
• Transition Probabilities for Symmetric Jump Processes
• A local-time correspondence for stochastic partial differential equations
• Burgers' system with a fractional Brownian random force
• Nash type inequalities for fractional powers of non-negative self-adjoint operators
• Harmonic Coordinates on Fractals with Finitely Ramified Cell Structure
• FUNCTIONAL INEQUALITIES, SEMIGROUP PROPERTIES AND SPECTRUM ESTIMATES
• Gradient-type noises I–partial and hybrid integrals
• Symmetric Markov chains on ℤ^{𝕕} with unbounded range
• Representation of fractional powers of infinitesimal generators of semigroups
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• Potential spaces on fractals
• Nonlinear diffusion equations on unbounded fractal domains