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Well-Posedness for Weak and Strong Solutions of Non-Homogeneous Initial Boundary Value Problems for Fractional Diffusion Equations
We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and...
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Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes
Atmospheric variables (temperature, velocity, etc.) are often decomposed into balanced and unbalanced components that represent low-frequency and...
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Seventy Five (Thousand) Unsolved Problems in Analysis and Partial Differential Equations
This is a collection of open problems concerning various areas in function theory, functional analysis, theory of linear and nonlinear partial...
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Superconvergence of immersed finite element methods for interface problems
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to...
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Gradient estimates for parabolic equations in generalized weighted Morrey spaces
We consider the Cauchy–Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg flat domain. The coefficients supposed...
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Generalized and Classical Solutions to a Characteristic Cauchy Problem with Hörmander Hypotheses
Classical solutions to a characteristic Cauchy problem studied by Hörmander are compared to the generalized ones obtained by a parametrized...
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On the Notion of Renormalized Solution to Nonlinear Parabolic Equations with General Measure Data
Here we introduce a new notion of renormalized solution to nonlinear parabolic problems with general measure data whose model is (\[\left\{...
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On the maximum principle for elliptic operators in weighted spaces
We establish a maximum principle for subsolutions of second order elliptic equations. In particular, we consider some linear operators with leading...
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Explicit estimates for solutions of nonlinear radiation-type problems
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with...
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Nonlinear gradient estimates for parabolic obstacle problems in non-smooth domains
We study a nonlinear parabolic equation with an irregular obstacle over a non-smooth domain and establish a global Calderón–Zygmund theory by proving...
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Solvability of the Dirichlet problem in W 2,p for a class of elliptic equations with singular data
We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.
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The Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains of the plane
This paper deals with the Dirichlet problem for second order linear elliptic equations in unbounded domains of the plane in weighted Sobolev spaces....
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Uniform Estimate of the Relative Free Energy by the Dissipation Rate for Finite Volume Discretized Reaction-Diffusion Systems
We prove a uniform Poincaré-like estimate of the relative free energy by the dissipation rate for implicit Euler, finite volume discretized...
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Diffraction problems for quasilinear parabolic systems with boundary intersecting interfaces
In this paper, we discuss the n -dimensional diffraction problem for weakly coupled quasilinear parabolic system on a bounded domain Ω, where the...
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Weighted L p -estimates for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains
We obtain a global weighted L p estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in...
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The Dirichlet Problem for Elliptic Equations with VMO Coefficients in Generalized Morrey Spaces
We consider the Dirichlet problem in a bounded smooth domain $$ \Omega \subset...