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Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 04/2017, Volume 56, Issue 2
Journal Article
Mathematische Annalen, ISSN 0025-5831, 02/2016, Volume 364, Issue 1-2, pp. 559 - 587
Journal Article
Mathematische Annalen, ISSN 0025-5831, 12/2015, Volume 363, Issue 3-4, pp. 1023 - 1052
Journal Article
Mathematische Annalen, ISSN 0025-5831, 2/2016, Volume 364, Issue 1, pp. 559 - 587
We derive an $$H_{0}^{s,p}(\text {curl};\varOmega )$$ H 0 s , p ( curl ; Ω ) estimate for the solutions of the Maxwell type equations modeled with anisotropic... 
35D30 | Mathematics, general | 78A25 | Mathematics | 35J25 | 35Q61
Journal Article
Science China Mathematics, ISSN 1674-7283, 7/2018, Volume 61, Issue 7, pp. 1219 - 1242
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation $$ - \Delta u = \left( {\int_\Omega... 
35A15 | Choquard equation | 35J60 | Hardy-Littlewood-Sobolev inequality | critical exponent | Mathematics | Applications of Mathematics | 35J25 | Brezis-Nirenberg problem | EXISTENCE | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | MULTIPLICITY | SCHRODINGER-EQUATION | CRITICAL SOBOLEV EXPONENTS | GROUND-STATE SOLUTIONS
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 08/2011, Volume 36, Issue 8, pp. 1353 - 1384
We investigate stable solutions of elliptic equations of the type where n ≥ 2, s ∈ (0, 1), λ ≥0 and f is any smooth positive superlinear function. The operator... 
Extremal solutions | Boundary reactions | Fractional operators | 35B45 | 47G30 | 53A05 | 35J25 | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | BOUNDARY | MINIMIZERS | Partial differential equations | Analysis of PDEs | Mathematics
Journal Article
Mathematische Annalen, ISSN 0025-5831, 12/2015, Volume 363, Issue 3, pp. 1023 - 1052
We establish an optimal $$W^{2,p(\cdot )}$$ W 2 , p ( · ) -estimate to the Dirichlet problem for an elliptic equation in nondivergence form with discontinuous... 
Mathematics, general | Mathematics | 46E35 | Primary 35J25 | Secondary 46E30
Journal Article
Mathematische Annalen, ISSN 0025-5831, 12/2015, Volume 363, Issue 3, pp. 1281 - 1306
If stiff inclusions are closely located, then the stress, which is the gradient of the solution, may become arbitrarily large as the distance between two... 
Mathematics, general | 74F15 | Mathematics | 74C20 | 35J25 | MATHEMATICS | FIBERS | ELECTRIC-FIELDS | ENHANCEMENT | PERFECT | SYSTEMS | EQUATION
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2019, Volume 16, Issue 6, pp. 1 - 22
We consider the second-order elliptic operator $$\begin{aligned} L =\Delta +(a-1)\sum _{i,j=1}^N\frac{x_ix_j}{|x|^2}D_{ij}+c\frac{x}{|x|^2}\cdot \nabla... 
Elliptic operators | discontinuous coefficients | kernel estimates | 35J70 | Mathematics, general | Mathematics | 35B50 | 35J25 | 47D07 | analytic semigroups
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 11/2018, Volume 18, Issue 4, pp. 775 - 783
In this paper, we study the regularizing effect of lower order terms in elliptic problems involving a Hardy potential. Concretely, our model problem is the... 
Regularizing Effect | Elliptic Equations | Lower Order Terms | Hardy Potential | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 6/2018, Volume 228, Issue 3, pp. 923 - 967
In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary... 
Fluid- and Aerodynamics | 35J60 | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | 35B65 | 35D40 | Physics, general | 35J25 | Physics | MATHEMATICS, APPLIED | DERIVATIVE PROBLEMS | MECHANICS | Mathematics - Analysis of PDEs
Journal Article
Complex Variables and Elliptic Equations, ISSN 1747-6933, 11/2019, Volume 64, Issue 11, pp. 1844 - 1853
We consider the semilinear elliptic problem: where is an open bounded subset, Under assumptions small we show that there exists a solution to this problem. The... 
positive solution | Hardy potential | Secondary 46E35 | 35J25 | Nonlinear elliptic equation | Primary 35J05 | EXISTENCE | MATHEMATICS | EQUATIONS
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 10/2017, Volume 42, Issue 10, pp. 1497 - 1509
In this note, we explore the validity of Wente-type estimates for Neumann boundary problems involving Jacobians. We show in particular that such estimates do... 
Conformal invariant problems | Neumann boundary conditions | 35B65 | integrability by compensation | 30C70 | 35J25 | Jacobians | MATHEMATICS | MATHEMATICS, APPLIED | Dirichlet problem
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 4/2019, Volume 70, Issue 2, pp. 1 - 18
In this work, we study the existence of nontrivial solutions for the following class of partial differential inclusion problem: $$\begin{aligned} -\Delta... 
Engineering | Mathematical Methods in Physics | Orlicz–Sobolev spaces | Discontinuous nonlinearity | 35A15 | 34A36 | Theoretical and Applied Mechanics | 35J25
Journal Article
Acta Mathematica Scientia, ISSN 0252-9602, 3/2019, Volume 39, Issue 2, pp. 357 - 368
This paper is devoted to the quasilinear equation $$\left\{ \begin{gathered}- div\left( {w_1 \left| {\nabla u} \right|^{p - 2} \nabla u} \right) = w_2 f\left(... 
nonexistence | Liouville theorems | 35B35 | Analysis | 35J92 | Mathematics, general | 35B53 | Mathematics | 35J25 | quasilinear equations | stable solutions
Journal Article
Manuscripta Mathematica, ISSN 0025-2611, 3/2016, Volume 149, Issue 3, pp. 339 - 346
A Wiener-type condition for the continuity at the boundary points of Q-minima, is established, in terms of the divergence of a suitable Wiener integral. 
Geometry | Secondary 35B45 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 35J25 | Primary 49K20 | MATHEMATICS | EQUATIONS | REGULARITY | Mathematics - Analysis of PDEs
Journal Article
Mathematische Annalen, ISSN 0025-5831, 12/2015, Volume 363, Issue 3, pp. 953 - 971
In this paper we introduce a new type of symmetrization, which preserves the anisotropic perimeter of the level sets of a suitable concave smooth function, in... 
Mathematics, general | Mathematics | 35J25 | 35A23 | MATHEMATICS | EQUATIONS | BOUNDARY | CONVEX SYMMETRIZATION | ISOPERIMETRIC-INEQUALITIES | Anisotropy
Journal Article
Bulletin of Mathematical Sciences, ISSN 1664-3607, 8/2018, Volume 8, Issue 2, pp. 353 - 411
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 12/2014, Volume 21, Issue 6, pp. 885 - 914
In this paper we investigate the following Kirchhoff type elliptic boundary value problem involving a critical nonlinearity:... 
Analysis | Kirchhoff | Mathematics | Critical | Variational method | Elliptic | 35J25 | Primary 35J60 | Secondary 35J20 | EXISTENCE | MATHEMATICS, APPLIED | MULTIPLICITY | STABILITY | CRITICAL GROWTH | STANDING WAVES | COMPACTNESS
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 12/2016, Volume 23, Issue 6, pp. 1 - 34
We apply the compactness results obtained in the first part of this work, to prove existence and multiplicity results for finite energy solutions to the... 
Sobolev spaces of radial functions | Analysis | 35Q55 | Mathematics | Nonlinear elliptic equations | 35J25 | Primary 35J60 | Secondary 35J20 | Vanishing or unbounded potentials | Compact embeddings | MATHEMATICS, APPLIED | STATES | NONLINEAR SCHRODINGER-EQUATIONS | Cytokinins | Mathematics - Analysis of PDEs
Journal Article
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