Results 21 to 30 of about 402 (50)
Free boundary problems for Tumor Growth: a Viscosity solutions approach [PDF]
, 2015 The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free boundaries, which, in the absence of active motion, are generalized Hele-Shaw
Alt +14 more
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Nonsmooth viscosity solutions of elementary symmetric functions of the complex Hessian
, 2015 In this paper we prove the existence of nonsmooth viscosity solutions for Dirichlet problems involving elementary symmetric functions of the eigenvalues of the complex ...
Guidi, Chiara +2 more
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Convergence of nonlocal geometric flows to anisotropic mean curvature motion [PDF]
, 2018 We consider nonlocal curvature functionals associated with positive interaction kernels, and we show that local anisotropic mean curvature functionals can be retrieved in a blow-up limit from them.
Cesaroni, Annalisa, Pagliari, Valerio
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Starshapedeness for fully-nonlinear equations in Carnot groups [PDF]
, 2018 In this paper we establish the starshapedness of the level sets of the capacitary potential of a large class of fully-nonlinear equations for condensers in Carnot groups, once a natural notion of starshapedness has been introduced.
Dragoni, Federica +2 more
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, 2016 We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in $BV$, which is the energy space. We show existence of solutions in this energy space and then we prove that they are viscosity solutions in ...
A Briani +29 more
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On the regularizing effect for unbounded solutions of first-order Hamilton-Jacobi equations [PDF]
, 2015 We give a simplified proof of regularizing effects for first-order Hamilton-Jacobi Equations of the form $u\_t+H(x,t,Du)=0$ in $\R^N\times(0,+\infty)$ in the case where the idea is to first estimate $u\_t$.
Barles, Guy, Chasseigne, Emmanuel
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Numerical solution of a PDE arising from prediction with expert advice
European Journal of Applied MathematicsThis work investigates the online machine learning problem of prediction with expert advice in an adversarial setting through numerical analysis of, and experiments with, a related partial differential equation.
Jeff Calder +2 more
doaj +1 more source
Continuity of the Feynman-Kac formula for a generalized parabolic equation
, 2016 It is well-known since the work of Pardoux and Peng [12] that Backward Stochastic Differential Equations provide probabilistic formulae for the solution of (systems of) second order elliptic and parabolic equations, thus providing an extension of the ...
Pardoux, Etienne, Rascanu, Aurel
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Large Deviations for Non-Markovian Diffusions and a Path-Dependent Eikonal Equation [PDF]
, 2014 This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic differential equations with random coefficients.
Ma, Jin +3 more
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Games for eigenvalues of the Hessian and concave/convex envelopes
, 2018 We study the PDE $\lambda_j(D^2 u) = 0$, in $\Omega$, with $u=g$, on $\partial \Omega$. Here $\lambda_1(D^2 u) \leq ... \leq \lambda_N (D^2 u)$ are the ordered eigenvalues of the Hessian $D^2 u$. First, we show a geometric interpretation of the viscosity
Blanc, Pablo, Rossi, Julio D.
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