Weak formulations of the nonlinear Poisson-Boltzmann equation in biomolecular electrostatics
From MaRDI portal
Publication:2669361
DOI10.1016/j.jmaa.2022.126065zbMath1485.35127arXiv2012.06437OpenAlexW3111870186MaRDI QIDQ2669361
Svetoslav Nakov, José A. Iglesias
Publication date: 9 March 2022
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.06437
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear elliptic equations (35J61) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
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- Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
- Blow-up theories for semilinear parabolic equations
- Approximated solutions of equations with \(L^ 1\) data. Application to the \(H\)-convergence of quasilinear parabolic equations
- Boundedness of minimizers
- On a nonlinear partial differential equation having natural growth terms and unbounded solution
- Nonlinear elliptic and parabolic equations involving measure data
- Functional analysis, Sobolev spaces and partial differential equations
- Existence of a solution to a coupled elliptic system
- A property of nonlinear elliptic equations when the right-hand side is a measure
- Elliptic partial differential equations of second order
- Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term.
- Strong stability results for solutions of elliptic equations with power-like lower order terms and measure data
- Semi-linear second-order elliptic equations in \(L^1\)
- Non-uniformly elliptic equations with natural growth in the gradient
- Nonlinear problems related to the Thomas-Fermi equation
- Accurate evaluation of electrostatics for macromolecules in solution
- Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
- Reliable computer simulation methods for electrostatic biomolecular models based on the Poisson-Boltzmann equation
- Optimal regularity for elliptic transmission problems including \(C^1\) interfaces
- Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
- Semilinear equations with exponential nonlinearity and measure data
- Erratum: “Minimization of Electrostatic Free Energy and the Poisson–Boltzmann Equation for Molecular Solvation with Implicit Solvent"
- Uniqueness Criteria for the Adjoint Equation in State-Constrained Elliptic Optimal Control
- Best constants in some exponential Sobolev inequalities
- Minimization of Electrostatic Free Energy and the Poisson–Boltzmann Equation for Molecular Solvation with Implicit Solvent
- Boundary Value Problems for Strongly Nonlinear Elliptic Equations
- Nonlinear Elliptic Equations with Right Hand Side Measures
- $L^\infty $ Estimate for Some Nonlinear Elliptic Partial Differential Equations and Application to an Existence Result
- A Finite Volume Scheme for a Noncoercive Elliptic Equation with Measure Data
- An Introduction to Variational Inequalities and Their Applications
- Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
- A First Course in Sobolev Spaces
- Finite Element Methods for Maxwell's Equations
- STABILITY PROPERTIES, EXISTENCE, AND NONEXISTENCE OF RENORMALIZED SOLUTIONS FOR ELLIPTIC EQUATIONS WITH MEASURE DATA1*
- The Finite Element Approximation of the Nonlinear Poisson–Boltzmann Equation
- Nonlinear elliptic equations with measures revisited
- Direct methods in the calculus of variations
