Add to ORKGWe provide some counterexamples concerning the uniqueness and regularity of weak solutions to the initial-boundary value problem for gradient flows of certain strongly polyconvex functionals by showing that such a problem can possess a trivial classical solution as well as infinitely many weak solutions that are nowhere smooth. Such polyconvex functions have been constructed in the previous work, and the nonuniqueness and nonregularity will be achieved by reformulating the gradient flow as a space-time partial differential relation and then using the convex integration method to construct certain strongly convergent sequences of subsolutions that have a uniform control on the local essential oscillations of their spatial gradients.Comment: ...
International audienceWe prove the existence of weak solutions to a system of two diffusion equation...
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space governed b...
We give an example of a smooth function f : ℝ2×2 → ℝ, which is not polyconvex and which has the prop...
We are interested in the gradient flow of a general first order convex functional with respect to th...
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This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space governed by ...
We investigate fundamental properties of the proximal point algorithm for Lipschitz convex functions...
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space $H$ $$ u?(...
AbstractIn this note a simple counter example shows that the proof of Lemma 3.3 in [1, W. Cheng, Y. ...
We consider the geometric evolution problem of entire graphs moving by fractional mean curvature. Fo...
We study families of porous medium equation with nonlocal pressure. We construct their weak solution...
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We study the L2-gradient flow of the nonconvex functional F phi(u) := 1/2 integral((0,1)) phi(u(x)) ...
In this note we solve a problem posed by J. M. Ball in [3] about the uniqueness of smooth equilibriu...
In this work I show that minimizers and other equilibrium points of certain classes of functionals i...
International audienceWe prove the existence of weak solutions to a system of two diffusion equation...
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space governed b...
We give an example of a smooth function f : ℝ2×2 → ℝ, which is not polyconvex and which has the prop...
We are interested in the gradient flow of a general first order convex functional with respect to th...
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraints. ...
This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space governed by ...
We investigate fundamental properties of the proximal point algorithm for Lipschitz convex functions...
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space $H$ $$ u?(...
AbstractIn this note a simple counter example shows that the proof of Lemma 3.3 in [1, W. Cheng, Y. ...
We consider the geometric evolution problem of entire graphs moving by fractional mean curvature. Fo...
We study families of porous medium equation with nonlocal pressure. We construct their weak solution...
We disclose an interesting connection between the gradient flow of a C 2 - smooth function ψ and ...
We study the L2-gradient flow of the nonconvex functional F phi(u) := 1/2 integral((0,1)) phi(u(x)) ...
In this note we solve a problem posed by J. M. Ball in [3] about the uniqueness of smooth equilibriu...
In this work I show that minimizers and other equilibrium points of certain classes of functionals i...
International audienceWe prove the existence of weak solutions to a system of two diffusion equation...
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space governed b...
We give an example of a smooth function f : ℝ2×2 → ℝ, which is not polyconvex and which has the prop...