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

  title={Space–time analyticity of weak solutions to linear parabolic systems with variable coefficients},
  author={Peter Tak{\'a}{\vc}},
  journal={Journal of Functional Analysis},
  • P. Takáč
  • Published 1 July 2012
  • Mathematics
  • Journal of Functional Analysis
Space-Time Analyticity of Weak Solutions to Semilinear Parabolic Systems with Variable Coefficients
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
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
Monotone methods in counterparty risk models with non-linear Black-Scholes-type equations
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
On the Heston Model with Stochastic Volatility: Analytic Solutions and Complete Markets
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
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.
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
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
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


Space Analyticity for the Navier–Stokes and Related Equations with Initial Data inLp
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
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
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
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
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
Function theory of several complex variables
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,