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Nonnegative weak solution for a periodic parabolic equation with bounded Radon measure
The purpose of this work is to study a class of periodic parabolic equations having a critical growth nonlinearity with respect to the gradient and...
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Radon Measure Solutions to Riemann Problems for Isentropic Compressible Euler Equations of Polytropic Gases
We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures, and the solutions admit...
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Existence and asymptotic behavior of Radon measure-valued solutions for a class of nonlinear parabolic equations
In this paper we address the weak Radon measure-valued solutions associated with the Young measure for a class of nonlinear parabolic equations with...
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The Radon-Carleman Problem
In view of the pioneering work and fundamental contributions of Johann Karl August Radon and Torsten Carleman, we find it appropriate to label the...
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Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets
AbstractSome questions concerning the inversion of the classical and generalized integral Radon transforms are discussed. The main issue is to...
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Renormalized Solution to Nonlinear Elliptic Equations with Measure Data in Musielak Spaces
This article is concerned with the existence of renormalized solution for an elliptic equation having two lower order terms and measure data in...
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Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions
We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ d with d ≥ 1 and show that, even when they start at some...
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Quaternionic Monge–Ampère Measure on Pluripolar Set
In this paper, we prove that in a hyperconvex domain Ω in ℍ n , if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure,...
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Inequalities for the derivatives of the Radon transform on convex bodies
It was proved in [22] that the sup-norm of the Radon transform of an arbitrary probability density on an origin-symmetric convex body of volume 1 is...
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Support theorems for Funk-type isodistant Radon transforms on constant curvature spaces
A connected maximal submanifold in a constant curvature space is called isodistant if its points are in equal distances from a totally geodesic of...
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A level line of the Gaussian free field with measure-valued boundary conditions
In this article, we construct samples of Schramm-Loewner-evolution-like curves out of samples of the conformal loop ensemble and Poisson point...
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A critical fractional choquard problem involving a singular nonlinearity and a radon measure
This article concerns about the existence of a positive SOLA (Solutions Obtained as Limits of Approximations) for the following singular critical...
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On weak (measure valued)–strong uniqueness for Navier–Stokes–Fourier system with Dirichlet boundary condition
In this article, our goal is to define a measure valued solution of compressible Navier–Stokes–Fourier system for a heat conducting fluid with...
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Solution of the Far Field Refractor Problem \( \kappa <1\)
This chapter solves the refractor problem in the far field. The notions of refractor measure, refractor map** and weak solution are introduced. The...
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Segmentation in Measure Spaces
We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most...
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Measure Solutions for Impulsive Systems
This chapter studies evolution equations subject to impulsive forces, considering the questions of existence and uniqueness of measure-valued...
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Dualities, Measure Concentration and Transportation
In these three lectures we shall review and discuss in detail the fascinating connection between duality transforms (mainly Legendre and polarity,...
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Measure-Valued Optimal Control for Size-Structured Population Models with Diffusion
We consider a control problem to maximize a profit from harvesting in agriculture or aquaculture, where the population is governed by size-structured...