# Space–time analyticity of weak solutions to linear parabolic systems with variable coefficients

@article{Tak2012SpacetimeAO, title={Space–time analyticity of weak solutions to linear parabolic systems with variable coefficients}, author={Peter Tak{\'a}{\vc}}, journal={Journal of Functional Analysis}, year={2012}, volume={263}, pages={50-88} }

## 9 Citations

Space-Time Analyticity of Weak Solutions to Semilinear Parabolic Systems with Variable Coefficients

- Mathematics
- 2020

Analytic smooth solutions of a general, strongly parabolic semilinear Cauchy problem of 2m-th order in R × (0, T ) with analytic coefficients (in space and time variables) and analytic initial data…

Analyticity of Solutions to Parabolic Evolutions and Applications

- MathematicsSIAM J. Math. Anal.
- 2017

We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with analytic coefficients near the initial time. We apply the estimates to obtain…

On the Heston Model with Stochastic Volatility: Analytic Solutions and Complete Markets

- Mathematics
- 2017

We study the Heston model for pricing European options on stocks with stochastic volatility. This is a Black-Scholes-type equation whose spatial domain for the logarithmic stock price x ∈ R and the…

Observations from measurable sets and applications

- Mathematics
- 2014

We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with time-independent coefficients and apply them to obtain observability inequalities for…

The Heston stochastic volatility model has a boundary trace at zero volatility.

- Mathematics
- 2020

We establish boundary regularity results in H\"older spaces for the degenerate parabolic problem obtained from the Heston stochastic volatility model in Mathematical Finance set up in the spatial…

Existence of an endogenously complete equilibrium driven by a diffusion

- EconomicsFinance Stochastics
- 2015

The existence of complete Radner equilibria is established in an economy whose parameters are driven by a diffusion process and the time-inhomogeneous case is treated.

Quantitative estimates of analyticity, applications and elliptic regularity end-points

- Art
- 2016

En esta tesis se prueban acotaciones inferiores para el radio de convergencia de la serie de Taylor enlas variables espaciales de soluciones de ecuaciones parabolicas cuyos coeficientes son…

Monotone methods in counterparty risk models with non-linear Black-Scholes-type equations

- Mathematics
- 2022

A nonlinear Black-Scholes-type equation is studied within counterparty risk models. The classical hypothesis on the uniform Lipschitz-continuity of the nonlinear reaction function allows for an…

## References

SHOWING 1-10 OF 61 REFERENCES

Space Analyticity for the Navier–Stokes and Related Equations with Initial Data inLp

- Mathematics
- 1998

Abstract We introduce a method of estimating the space analyticity radius of solutions for the Navier–Stokes and related equations in terms of L p and L ∞ norms of the initial data. The method…

Regularity in Time of Solutions to Nonlinear Schrödinger Equations

- Mathematics
- 1995

Abstract In this paper we consider the regularity of solutions to nonlinear Schrodinger equations (NLS), i ∂ t u + 1 2 Δu = F(u, u ), (t, x) ∈ R × R n , u(0) = φ, x ∈ R n , where F is a polynomial of…

Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation

- Mathematics
- 1994

Some analytic smoothing properties of a general strongly coupled, strongly parabolic semilinear system of order $2m$ in $realnos^D times (0,T)$ with analytic entries are investigated. These…

Smoothing effect of small analytic solutions to nonlinear Schrödinger equations

- Mathematics
- 1992

We consider the initial value problem for nonlinear Schrodinger equations in Rn(~2): and for any complex number o with ~= 1. It is shown that global solutions of (*) have a smoothing property.…

Strongly continuous semigroups, weak solutions, and the variation of constants formula

- Mathematics
- 1977

Let A be a densely defined closed linear operator on a Banach space X, and let f E L'(O,r;X). A definition of weak solutions of the equation u = Au + f(t) is given. It is shown that a necessary and…

Global solutions of the derivative Schrödinger equation in a class of functions analytic in a strip

- Mathematics
- 2006

Function theory of several complex variables

- Mathematics
- 1982

Some integral formulas. Subharmonicity and its applications. Convexity. Hormander's solution of the equation. Solution of the Levi problem and other applications of techniques. Cousin problems,…